The paper addresses the issue of H_(∞)couple-group consensus for a class of discrete-time stochastic multi-agent systems via output-feedback control.Both fixed and Markovian switching communication topologies are con...The paper addresses the issue of H_(∞)couple-group consensus for a class of discrete-time stochastic multi-agent systems via output-feedback control.Both fixed and Markovian switching communication topologies are considered.By employing linear transformations,the closed-loop systems are converted into reduced-order systems and the H_(∞)couplegroup consensus issue under consideration is changed into a stochastic H_(∞)control problem.New conditions for the mean-square asymptotic stability and H_(∞)performance of the reduced-order systems are proposed.On the basis of these conditions,constructive approaches for the design of the output-feedback control protocols are developed for the fixed communication topology and the Markovian switching communication topologies,respectively.Finally,two numerical examples are given to illustrate the applicability of the present design approaches.展开更多
This study addresses the fault detection problem in multi-agent systems(MASs)with additive faults and stochastic uncertainties.The main focus is on enhancing the fault detection capability of each agent through a coop...This study addresses the fault detection problem in multi-agent systems(MASs)with additive faults and stochastic uncertainties.The main focus is on enhancing the fault detection capability of each agent through a cooperative fault detection scheme,fostering cooperation between agents in two scenarios.For Gaussian uncertainties,one scheme is developed using the maximum likelihood estimation(MLE)matching expectation maximization(EM)algorithm.Additionally,a novel cooperative fault detection scheme is introduced to handle non-Gaussian uncertainties,where the cooperation mechanism among agents is determined by approximating non-Gaussian uncertainties using the Gaussian mixture model(GMM).The effectiveness and improvements of the proposed cooperative fault detection method are validated through numerical simulations.展开更多
Cooperative multi-agent reinforcement learning(MARL)is a key technology for enabling cooperation in complex multi-agent systems.It has achieved remarkable progress in areas such as gaming,autonomous driving,and multi-...Cooperative multi-agent reinforcement learning(MARL)is a key technology for enabling cooperation in complex multi-agent systems.It has achieved remarkable progress in areas such as gaming,autonomous driving,and multi-robot control.Empowering cooperative MARL with multi-task decision-making capabilities is expected to further broaden its application scope.In multi-task scenarios,cooperative MARL algorithms need to address 3 types of multi-task problems:reward-related multi-task,arising from different reward functions;multi-domain multi-task,caused by differences in state and action spaces,state transition functions;and scalability-related multi-task,resulting from the dynamic variation in the number of agents.Most existing studies focus on scalability-related multitask problems.However,with the increasing integration between large language models(LLMs)and multi-agent systems,a growing number of LLM-based multi-agent systems have emerged,enabling more complex multi-task cooperation.This paper provides a comprehensive review of the latest advances in this field.By combining multi-task reinforcement learning with cooperative MARL,we categorize and analyze the 3 major types of multi-task problems under multi-agent settings,offering more fine-grained classifications and summarizing key insights for each.In addition,we summarize commonly used benchmarks and discuss future directions of research in this area,which hold promise for further enhancing the multi-task cooperation capabilities of multi-agent systems and expanding their practical applications in the real world.展开更多
This paper addresses the consensus problem of nonlinear multi-agent systems subject to external disturbances and uncertainties under denial-ofservice(DoS)attacks.Firstly,an observer-based state feedback control method...This paper addresses the consensus problem of nonlinear multi-agent systems subject to external disturbances and uncertainties under denial-ofservice(DoS)attacks.Firstly,an observer-based state feedback control method is employed to achieve secure control by estimating the system's state in real time.Secondly,by combining a memory-based adaptive eventtriggered mechanism with neural networks,the paper aims to approximate the nonlinear terms in the networked system and efficiently conserve system resources.Finally,based on a two-degree-of-freedom model of a vehicle affected by crosswinds,this paper constructs a multi-unmanned ground vehicle(Multi-UGV)system to validate the effectiveness of the proposed method.Simulation results show that the proposed control strategy can effectively handle external disturbances such as crosswinds in practical applications,ensuring the stability and reliable operation of the Multi-UGV system.展开更多
This paper investigates the challenges associated with Unmanned Aerial Vehicle (UAV) collaborative search and target tracking in dynamic and unknown environments characterized by limited field of view. The primary obj...This paper investigates the challenges associated with Unmanned Aerial Vehicle (UAV) collaborative search and target tracking in dynamic and unknown environments characterized by limited field of view. The primary objective is to explore the unknown environments to locate and track targets effectively. To address this problem, we propose a novel Multi-Agent Reinforcement Learning (MARL) method based on Graph Neural Network (GNN). Firstly, a method is introduced for encoding continuous-space multi-UAV problem data into spatial graphs which establish essential relationships among agents, obstacles, and targets. Secondly, a Graph AttenTion network (GAT) model is presented, which focuses exclusively on adjacent nodes, learns attention weights adaptively and allows agents to better process information in dynamic environments. Reward functions are specifically designed to tackle exploration challenges in environments with sparse rewards. By introducing a framework that integrates centralized training and distributed execution, the advancement of models is facilitated. Simulation results show that the proposed method outperforms the existing MARL method in search rate and tracking performance with less collisions. The experiments show that the proposed method can be extended to applications with a larger number of agents, which provides a potential solution to the challenging problem of multi-UAV autonomous tracking in dynamic unknown environments.展开更多
Existing semi-supervisedmedical image segmentation algorithms use copy-paste data augmentation to correct the labeled-unlabeled data distribution mismatch.However,current copy-paste methods have three limitations:(1)t...Existing semi-supervisedmedical image segmentation algorithms use copy-paste data augmentation to correct the labeled-unlabeled data distribution mismatch.However,current copy-paste methods have three limitations:(1)training the model solely with copy-paste mixed pictures from labeled and unlabeled input loses a lot of labeled information;(2)low-quality pseudo-labels can cause confirmation bias in pseudo-supervised learning on unlabeled data;(3)the segmentation performance in low-contrast and local regions is less than optimal.We design a Stochastic Augmentation-Based Dual-Teaching Auxiliary Training Strategy(SADT),which enhances feature diversity and learns high-quality features to overcome these problems.To be more precise,SADT trains the Student Network by using pseudo-label-based training from Teacher Network 1 and supervised learning with labeled data,which prevents the loss of rare labeled data.We introduce a bi-directional copy-pastemask with progressive high-entropy filtering to reduce data distribution disparities and mitigate confirmation bias in pseudo-supervision.For the mixed images,Deep-Shallow Spatial Contrastive Learning(DSSCL)is proposed in the feature spaces of Teacher Network 2 and the Student Network to improve the segmentation capabilities in low-contrast and local areas.In this procedure,the features retrieved by the Student Network are subjected to a random feature perturbation technique.On two openly available datasets,extensive trials show that our proposed SADT performs much better than the state-ofthe-art semi-supervised medical segmentation techniques.Using only 10%of the labeled data for training,SADT was able to acquire a Dice score of 90.10%on the ACDC(Automatic Cardiac Diagnosis Challenge)dataset.展开更多
Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign cur...Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exchange rate (SER) models to determine the best combination of these models for Monte Carlo (MC) simulation pricing. In addition, we test the performance of all model variants with constant correlation as a benchmark. We find that a combination of GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER performs best. In addition, we analyze different discretization schemes and their results. In our simulations, the Milstein scheme yields the best balance between execution times and lower standard deviations of price estimates. Furthermore, we find that incorporating mean reversion into stochastic correlation and stochastic FX rate modeling is beneficial for MC simulation pricing. We improve the accuracy of our simulations by implementing antithetic variates variance reduction. Finally, we derive the correlation risk parameters Cora and Gora in our framework so that correlation hedging of quanto options can be performed.展开更多
The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding sto...The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.展开更多
In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained f...In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations(SDEs),based on which the loss function is built.The stochastic gradient descent method is applied in the neural network training.Numerical experiments demonstrate the effectiveness of our method.展开更多
In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat eq...In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.展开更多
Risk management often plays an important role in decision making un-der uncertainty.In quantitative risk management,assessing and optimizing risk metrics requires eficient computing techniques and reliable theoretical...Risk management often plays an important role in decision making un-der uncertainty.In quantitative risk management,assessing and optimizing risk metrics requires eficient computing techniques and reliable theoretical guarantees.In this pa-per,we introduce several topics on quantitative risk management and review some of the recent studies and advancements on the topics.We consider several risk metrics and study decision models that involve the metrics,with a main focus on the related com-puting techniques and theoretical properties.We show that stochastic optimization,as a powerful tool,can be leveraged to effectively address these problems.展开更多
This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
In this paper,we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options.Furthermore,we assume that the interest rates and the jump inte...In this paper,we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options.Furthermore,we assume that the interest rates and the jump intensities of the assets are stochastic.Under the proposed framework,first,we derive the analytical pricing formula for power options by using Fourier transform technique,Esscher transform and characteristic function.Then we provide the efficient approximation to calculate the analytical pricing formula of power options by using the FFT approach and examine the accuracy of the approximation by Monte Carlo simulation.Finally,we provide some sensitivity analysis of the model parameters to power options.Numerical examples show this model is suitable for empirical work in practice.展开更多
In this paper,the convergence of the split-step theta method for stochastic differential equations is analyzed using stochastic C-stability and stochastic B-consistency.The fact that the numerical scheme,which is both...In this paper,the convergence of the split-step theta method for stochastic differential equations is analyzed using stochastic C-stability and stochastic B-consistency.The fact that the numerical scheme,which is both stochastically C-stable and stochastically B-consistent,is convergent has been proved in a previous paper.In order to analyze the convergence of the split-step theta method(θ∈[1/2,1]),the stochastic C-stability and stochastic B-consistency under the condition of global monotonicity have been researched,and the rate of convergence 1/2 has been explored in this paper.It can be seen that the convergence does not require the drift function should satisfy the linear growth condition whenθ=1/2 Furthermore,the rate of the convergence of the split-step scheme for stochastic differential equations with additive noise has been researched and found to be 1.Finally,an example is given to illustrate the convergence with the theoretical results.展开更多
By adopting stochastic density functional theory(SDFT)and mixed stochastic-deterministic density functional theory(MDFT)methods,we perform first-principles calculations to predict the shock Hugoniot curves of boron(pr...By adopting stochastic density functional theory(SDFT)and mixed stochastic-deterministic density functional theory(MDFT)methods,we perform first-principles calculations to predict the shock Hugoniot curves of boron(pressure P=7.9×10^(3)-1.6×10^(6) GPa and temperature T=25-2800 eV),silicon(P=2.6×10^(3)-7.9×10^(5) GPa and T=21.5-1393 eV),and aluminum(P=5.2×10^(3)-9.0×10^(5) GPa and T=25-1393 eV)over wide ranges of pressure and temperature.In particular,we systematically investigate the impact of different cutoff radii in norm-conserving pseudopotentials on the calculated properties at elevated temperatures,such as pressure,ionization energy,and equation of state.By comparing the SDFT and MDFT results with those of other first-principles methods,such as extended first-principles molecular dynamics and path integral Monte Carlo methods,we find that the SDFT and MDFT methods show satisfactory precision,which advances our understanding of first-principles methods when applied to studies of matter at extremely high pressures and temperatures.展开更多
This paper mainly focuses on the velocity-constrained consensus problem of discrete-time heterogeneous multi-agent systems with nonconvex constraints and arbitrarily switching topologies,where each agent has first-ord...This paper mainly focuses on the velocity-constrained consensus problem of discrete-time heterogeneous multi-agent systems with nonconvex constraints and arbitrarily switching topologies,where each agent has first-order or second-order dynamics.To solve this problem,a distributed algorithm is proposed based on a contraction operator.By employing the properties of the stochastic matrix,it is shown that all agents’position states could converge to a common point and second-order agents’velocity states could remain in corresponding nonconvex constraint sets and converge to zero as long as the joint communication topology has one directed spanning tree.Finally,the numerical simulation results are provided to verify the effectiveness of the proposed algorithms.展开更多
This paper focuses on the problem of leaderfollowing consensus for nonlinear cascaded multi-agent systems.The control strategies for these systems are transformed into successive control problem schemes for lower-orde...This paper focuses on the problem of leaderfollowing consensus for nonlinear cascaded multi-agent systems.The control strategies for these systems are transformed into successive control problem schemes for lower-order error subsystems.A distributed consensus analysis for the corresponding error systems is conducted by employing recursive methods and virtual controllers,accompanied by a series of Lyapunov functions devised throughout the iterative process,which solves the leaderfollowing consensus problem of a class of nonlinear cascaded multi-agent systems.Specific simulation examples illustrate the effectiveness of the proposed control algorithm.展开更多
Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonanc...Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonance is still in the preliminary stage.In this paper,we focus on the stochastic resonance induced by memristor chaos,which enhances the dynamics of chaotic systems through the introduction of memristor and induces memristor stochastic resonance under certain conditions.First,the memristor chaos model is constructed,and the memristor stochastic resonance model is constructed by adjusting the parameters of the memristor chaos model.Second,the combination of dynamic analysis and experimental verification is used to analyze the memristor stochastic resonance and to investigate the trend of the output signal of the system under different amplitudes of the input signal.Finally,the practicality and reliability of the constructed model are further verified through the design and testing of the analog circuit,which provides strong support for the practical application of the memristor chaos-induced stochastic resonance model.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61503002 and 61573008)
文摘The paper addresses the issue of H_(∞)couple-group consensus for a class of discrete-time stochastic multi-agent systems via output-feedback control.Both fixed and Markovian switching communication topologies are considered.By employing linear transformations,the closed-loop systems are converted into reduced-order systems and the H_(∞)couplegroup consensus issue under consideration is changed into a stochastic H_(∞)control problem.New conditions for the mean-square asymptotic stability and H_(∞)performance of the reduced-order systems are proposed.On the basis of these conditions,constructive approaches for the design of the output-feedback control protocols are developed for the fixed communication topology and the Markovian switching communication topologies,respectively.Finally,two numerical examples are given to illustrate the applicability of the present design approaches.
基金supported in part by the National Natural Science Foundation of China under Grant Nos.62103304 and 62177036Shanghai Sailing Program under Grant No.21YF1450500+1 种基金Shanghai Municipal Science and Technology Major Project under Grant No.2021SHZDZX0100Shanghai Municipal Commission of Science and Technology Project under Grant No.19511132101。
文摘This study addresses the fault detection problem in multi-agent systems(MASs)with additive faults and stochastic uncertainties.The main focus is on enhancing the fault detection capability of each agent through a cooperative fault detection scheme,fostering cooperation between agents in two scenarios.For Gaussian uncertainties,one scheme is developed using the maximum likelihood estimation(MLE)matching expectation maximization(EM)algorithm.Additionally,a novel cooperative fault detection scheme is introduced to handle non-Gaussian uncertainties,where the cooperation mechanism among agents is determined by approximating non-Gaussian uncertainties using the Gaussian mixture model(GMM).The effectiveness and improvements of the proposed cooperative fault detection method are validated through numerical simulations.
基金The National Natural Science Foundation of China(62136008,62293541)The Beijing Natural Science Foundation(4232056)The Beijing Nova Program(20240484514).
文摘Cooperative multi-agent reinforcement learning(MARL)is a key technology for enabling cooperation in complex multi-agent systems.It has achieved remarkable progress in areas such as gaming,autonomous driving,and multi-robot control.Empowering cooperative MARL with multi-task decision-making capabilities is expected to further broaden its application scope.In multi-task scenarios,cooperative MARL algorithms need to address 3 types of multi-task problems:reward-related multi-task,arising from different reward functions;multi-domain multi-task,caused by differences in state and action spaces,state transition functions;and scalability-related multi-task,resulting from the dynamic variation in the number of agents.Most existing studies focus on scalability-related multitask problems.However,with the increasing integration between large language models(LLMs)and multi-agent systems,a growing number of LLM-based multi-agent systems have emerged,enabling more complex multi-task cooperation.This paper provides a comprehensive review of the latest advances in this field.By combining multi-task reinforcement learning with cooperative MARL,we categorize and analyze the 3 major types of multi-task problems under multi-agent settings,offering more fine-grained classifications and summarizing key insights for each.In addition,we summarize commonly used benchmarks and discuss future directions of research in this area,which hold promise for further enhancing the multi-task cooperation capabilities of multi-agent systems and expanding their practical applications in the real world.
基金The National Natural Science Foundation of China(W2431048)The Science and Technology Research Program of Chongqing Municipal Education Commission,China(KJZDK202300807)The Chongqing Natural Science Foundation,China(CSTB2024NSCQQCXMX0052).
文摘This paper addresses the consensus problem of nonlinear multi-agent systems subject to external disturbances and uncertainties under denial-ofservice(DoS)attacks.Firstly,an observer-based state feedback control method is employed to achieve secure control by estimating the system's state in real time.Secondly,by combining a memory-based adaptive eventtriggered mechanism with neural networks,the paper aims to approximate the nonlinear terms in the networked system and efficiently conserve system resources.Finally,based on a two-degree-of-freedom model of a vehicle affected by crosswinds,this paper constructs a multi-unmanned ground vehicle(Multi-UGV)system to validate the effectiveness of the proposed method.Simulation results show that the proposed control strategy can effectively handle external disturbances such as crosswinds in practical applications,ensuring the stability and reliable operation of the Multi-UGV system.
基金supported by the National Natural Science Foundation of China(Nos.12272104,U22B2013).
文摘This paper investigates the challenges associated with Unmanned Aerial Vehicle (UAV) collaborative search and target tracking in dynamic and unknown environments characterized by limited field of view. The primary objective is to explore the unknown environments to locate and track targets effectively. To address this problem, we propose a novel Multi-Agent Reinforcement Learning (MARL) method based on Graph Neural Network (GNN). Firstly, a method is introduced for encoding continuous-space multi-UAV problem data into spatial graphs which establish essential relationships among agents, obstacles, and targets. Secondly, a Graph AttenTion network (GAT) model is presented, which focuses exclusively on adjacent nodes, learns attention weights adaptively and allows agents to better process information in dynamic environments. Reward functions are specifically designed to tackle exploration challenges in environments with sparse rewards. By introducing a framework that integrates centralized training and distributed execution, the advancement of models is facilitated. Simulation results show that the proposed method outperforms the existing MARL method in search rate and tracking performance with less collisions. The experiments show that the proposed method can be extended to applications with a larger number of agents, which provides a potential solution to the challenging problem of multi-UAV autonomous tracking in dynamic unknown environments.
基金supported by the Natural Science Foundation of China(No.41804112,author:Chengyun Song).
文摘Existing semi-supervisedmedical image segmentation algorithms use copy-paste data augmentation to correct the labeled-unlabeled data distribution mismatch.However,current copy-paste methods have three limitations:(1)training the model solely with copy-paste mixed pictures from labeled and unlabeled input loses a lot of labeled information;(2)low-quality pseudo-labels can cause confirmation bias in pseudo-supervised learning on unlabeled data;(3)the segmentation performance in low-contrast and local regions is less than optimal.We design a Stochastic Augmentation-Based Dual-Teaching Auxiliary Training Strategy(SADT),which enhances feature diversity and learns high-quality features to overcome these problems.To be more precise,SADT trains the Student Network by using pseudo-label-based training from Teacher Network 1 and supervised learning with labeled data,which prevents the loss of rare labeled data.We introduce a bi-directional copy-pastemask with progressive high-entropy filtering to reduce data distribution disparities and mitigate confirmation bias in pseudo-supervision.For the mixed images,Deep-Shallow Spatial Contrastive Learning(DSSCL)is proposed in the feature spaces of Teacher Network 2 and the Student Network to improve the segmentation capabilities in low-contrast and local areas.In this procedure,the features retrieved by the Student Network are subjected to a random feature perturbation technique.On two openly available datasets,extensive trials show that our proposed SADT performs much better than the state-ofthe-art semi-supervised medical segmentation techniques.Using only 10%of the labeled data for training,SADT was able to acquire a Dice score of 90.10%on the ACDC(Automatic Cardiac Diagnosis Challenge)dataset.
文摘Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exchange rate (SER) models to determine the best combination of these models for Monte Carlo (MC) simulation pricing. In addition, we test the performance of all model variants with constant correlation as a benchmark. We find that a combination of GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER performs best. In addition, we analyze different discretization schemes and their results. In our simulations, the Milstein scheme yields the best balance between execution times and lower standard deviations of price estimates. Furthermore, we find that incorporating mean reversion into stochastic correlation and stochastic FX rate modeling is beneficial for MC simulation pricing. We improve the accuracy of our simulations by implementing antithetic variates variance reduction. Finally, we derive the correlation risk parameters Cora and Gora in our framework so that correlation hedging of quanto options can be performed.
基金Supported by the National Natural Science Foundation of China(10671182)。
文摘The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.
基金Supported by the National Natural Science Foundation of China(11971458,11471310)。
文摘In this paper,we propose a neural network approach to learn the parameters of a class of stochastic Lotka-Volterra systems.Approximations of the mean and covariance matrix of the observational variables are obtained from the Euler-Maruyama discretization of the underlying stochastic differential equations(SDEs),based on which the loss function is built.The stochastic gradient descent method is applied in the neural network training.Numerical experiments demonstrate the effectiveness of our method.
基金Partially supported by Postgraduate Research and Practice Innovation Program of Jiangsu Province(Nos.KYCX22-2211,KYCX22-2205)。
文摘In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.
文摘Risk management often plays an important role in decision making un-der uncertainty.In quantitative risk management,assessing and optimizing risk metrics requires eficient computing techniques and reliable theoretical guarantees.In this pa-per,we introduce several topics on quantitative risk management and review some of the recent studies and advancements on the topics.We consider several risk metrics and study decision models that involve the metrics,with a main focus on the related com-puting techniques and theoretical properties.We show that stochastic optimization,as a powerful tool,can be leveraged to effectively address these problems.
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
文摘In this paper,we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options.Furthermore,we assume that the interest rates and the jump intensities of the assets are stochastic.Under the proposed framework,first,we derive the analytical pricing formula for power options by using Fourier transform technique,Esscher transform and characteristic function.Then we provide the efficient approximation to calculate the analytical pricing formula of power options by using the FFT approach and examine the accuracy of the approximation by Monte Carlo simulation.Finally,we provide some sensitivity analysis of the model parameters to power options.Numerical examples show this model is suitable for empirical work in practice.
基金Supported by the National Natural Science Foundation of China (Grant No. 12301521)the Natural Science Foundation of Shanxi Province (Grant No. 20210302124081)。
文摘In this paper,the convergence of the split-step theta method for stochastic differential equations is analyzed using stochastic C-stability and stochastic B-consistency.The fact that the numerical scheme,which is both stochastically C-stable and stochastically B-consistent,is convergent has been proved in a previous paper.In order to analyze the convergence of the split-step theta method(θ∈[1/2,1]),the stochastic C-stability and stochastic B-consistency under the condition of global monotonicity have been researched,and the rate of convergence 1/2 has been explored in this paper.It can be seen that the convergence does not require the drift function should satisfy the linear growth condition whenθ=1/2 Furthermore,the rate of the convergence of the split-step scheme for stochastic differential equations with additive noise has been researched and found to be 1.Finally,an example is given to illustrate the convergence with the theoretical results.
基金supported by the National Key R&D Program of China under Grant No.2025YFB3003603the National Natural Science Foundation of China under Grant Nos.12135002 and 12105209.
文摘By adopting stochastic density functional theory(SDFT)and mixed stochastic-deterministic density functional theory(MDFT)methods,we perform first-principles calculations to predict the shock Hugoniot curves of boron(pressure P=7.9×10^(3)-1.6×10^(6) GPa and temperature T=25-2800 eV),silicon(P=2.6×10^(3)-7.9×10^(5) GPa and T=21.5-1393 eV),and aluminum(P=5.2×10^(3)-9.0×10^(5) GPa and T=25-1393 eV)over wide ranges of pressure and temperature.In particular,we systematically investigate the impact of different cutoff radii in norm-conserving pseudopotentials on the calculated properties at elevated temperatures,such as pressure,ionization energy,and equation of state.By comparing the SDFT and MDFT results with those of other first-principles methods,such as extended first-principles molecular dynamics and path integral Monte Carlo methods,we find that the SDFT and MDFT methods show satisfactory precision,which advances our understanding of first-principles methods when applied to studies of matter at extremely high pressures and temperatures.
基金2024 Jiangsu Province Youth Science and Technology Talent Support Project2024 Yancheng Key Research and Development Plan(Social Development)projects,“Research and Application of Multi Agent Offline Distributed Trust Perception Virtual Wireless Sensor Network Algorithm”and“Research and Application of a New Type of Fishery Ship Safety Production Monitoring Equipment”。
文摘This paper mainly focuses on the velocity-constrained consensus problem of discrete-time heterogeneous multi-agent systems with nonconvex constraints and arbitrarily switching topologies,where each agent has first-order or second-order dynamics.To solve this problem,a distributed algorithm is proposed based on a contraction operator.By employing the properties of the stochastic matrix,it is shown that all agents’position states could converge to a common point and second-order agents’velocity states could remain in corresponding nonconvex constraint sets and converge to zero as long as the joint communication topology has one directed spanning tree.Finally,the numerical simulation results are provided to verify the effectiveness of the proposed algorithms.
基金National Natural Science Foundation of China(No.12071370)。
文摘This paper focuses on the problem of leaderfollowing consensus for nonlinear cascaded multi-agent systems.The control strategies for these systems are transformed into successive control problem schemes for lower-order error subsystems.A distributed consensus analysis for the corresponding error systems is conducted by employing recursive methods and virtual controllers,accompanied by a series of Lyapunov functions devised throughout the iterative process,which solves the leaderfollowing consensus problem of a class of nonlinear cascaded multi-agent systems.Specific simulation examples illustrate the effectiveness of the proposed control algorithm.
文摘Memristor chaotic research has become a hotspot in the academic world.However,there is little exploration combining memristor and stochastic resonance,and the correlation research between chaos and stochastic resonance is still in the preliminary stage.In this paper,we focus on the stochastic resonance induced by memristor chaos,which enhances the dynamics of chaotic systems through the introduction of memristor and induces memristor stochastic resonance under certain conditions.First,the memristor chaos model is constructed,and the memristor stochastic resonance model is constructed by adjusting the parameters of the memristor chaos model.Second,the combination of dynamic analysis and experimental verification is used to analyze the memristor stochastic resonance and to investigate the trend of the output signal of the system under different amplitudes of the input signal.Finally,the practicality and reliability of the constructed model are further verified through the design and testing of the analog circuit,which provides strong support for the practical application of the memristor chaos-induced stochastic resonance model.
