Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is inve...Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is investigated in this paper.First,sufficient conditions are proposed in terms of stochastic Lyapunov stability theory,It o differential rule and linear matrix inequality technology.The corresponding controller design is then cast into a convex optimization problem.Attention is focused on constructing an admissible controller,which guarantees that the closed-loop repetitive processes are mean-square asymptotically stable and have a prespecified H-infinity performance γ with respect to all energy-bounded input signals.A numerical example illustrates the effectiveness of the proposed design scheme.展开更多
This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix i...This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.展开更多
This paper deals with the problems of robust reliable exponential stabilization and robust stochastic stabilization with H-infinity performance for a class of nonlinear uncertain time-delay stochastic systems with Mar...This paper deals with the problems of robust reliable exponential stabilization and robust stochastic stabilization with H-infinity performance for a class of nonlinear uncertain time-delay stochastic systems with Markovian jumping parameters. The time delays are assumed to be dependent on the system modes. Delay-dependent conditions for the solvability of these problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that the desired state feedback controller can be designed by solving a set of linear matrix inequalities. Finally, the simulation is provided to demonstrate the effectiveness of the proposed methods.展开更多
This paper investigates the problem of robust L1 model reduction for continuous-time uncertain stochastic time-delay systems. For a given mean-square stable system, our purpose is to construct reduced-order systems, s...This paper investigates the problem of robust L1 model reduction for continuous-time uncertain stochastic time-delay systems. For a given mean-square stable system, our purpose is to construct reduced-order systems, such that the error system between these two models is mean-square asymptotically stable and has a guaranteed L1 (also called peak-to-peak) performance. The peak-to-peak gain criterion is first established for stochastic time-delay systems, and the corresponding model reduction problem is solved by using projection lemma. Sufficient conditions are obtained for the existence of admissible reduced-order models in terms of linear matrix inequalities (LMIs) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by standard numerical software. In addition, the development of reduced-order models with special structures, such as the delay-free model, is also presented. The efficiency of the proposed methods is demonstrated via a numerical example.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
A stochastic stage-structure predator-prey system with impulsive effect is investigated.First,we build the corresponding system without impulse in order to demonstrate the existence and uniqueness of the global positi...A stochastic stage-structure predator-prey system with impulsive effect is investigated.First,we build the corresponding system without impulse in order to demonstrate the existence and uniqueness of the global positive solution.Second,by selecting an appropriate Lyapunov function,we provide the sufficient condition for the existence of a positive T-periodic solution.Finally,numerical simulations illustrate our theoretical results,which show that the impulse or the white noises can result in the extinction of the predator in a certain condition.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 study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x...In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.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
The heavy quarks present in the quark-gluon plasma(QGP)can act as a probe of relativistic heavy ion collisions as they retain the memory of their interaction history.In a previous study,a stochastic Schrödinger e...The heavy quarks present in the quark-gluon plasma(QGP)can act as a probe of relativistic heavy ion collisions as they retain the memory of their interaction history.In a previous study,a stochastic Schrödinger equation(SSE)has been applied to describe the evolution of heavy quarks,where an external field with random phases is used to simulate the thermal medium.In this work,we study the connection between the SSE and the Boltzmann transport equation(BE)approach in the Keldysh Green’s function formalism.By comparing the Green’s function of the heavy quark from the SSE and the Keldysh Green’s functions leading to the Boltzmann equation,we demonstrate that the SSE is consistent with the Boltzmann equation in the weak coupling limit.We subsequently confirm their consistency through numerical calculations.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
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
Intelligent Traffic Management(ITM)has progressively developed into a critical component of modern transportation networks,significantly enhancing traffic flow and reducing congestion in urban environments.This resear...Intelligent Traffic Management(ITM)has progressively developed into a critical component of modern transportation networks,significantly enhancing traffic flow and reducing congestion in urban environments.This research proposes an enhanced framework that leverages Deep Q-Learning(DQL),Game Theory(GT),and Stochastic Optimization(SO)to tackle the complex dynamics in transportation networks.The DQL component utilizes the distribution of traffic conditions for epsilon-greedy policy formulation and action and choice reward calculation,ensuring resilient decision-making.GT models the interaction between vehicles and intersections through probabilistic distributions of various features to enhance performance.Results demonstrate that the proposed framework is a scalable solution for dynamic optimization in transportation networks.展开更多
基金supported by the Natural Science Foundation of Heilongjiang Province(No.F200504)
文摘Repetitive processes are a distinct class of 2D systems of both theoretic and practical interest.The robust H-infinity control problem for uncertain stochastic time-delay linear continuous repetitive processes is investigated in this paper.First,sufficient conditions are proposed in terms of stochastic Lyapunov stability theory,It o differential rule and linear matrix inequality technology.The corresponding controller design is then cast into a convex optimization problem.Attention is focused on constructing an admissible controller,which guarantees that the closed-loop repetitive processes are mean-square asymptotically stable and have a prespecified H-infinity performance γ with respect to all energy-bounded input signals.A numerical example illustrates the effectiveness of the proposed design scheme.
基金This work was supported by the National Natural Science Foundation of China(No.60474013)Specialized Research Fund for the Doctoral Program of Higher Education (No. 20050424002)the Doctoral Foundation of Shandong Province (No. 2004BS01010)
文摘This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.
基金the National Natural Science Foundation of China (No.60074007).
文摘This paper deals with the problems of robust reliable exponential stabilization and robust stochastic stabilization with H-infinity performance for a class of nonlinear uncertain time-delay stochastic systems with Markovian jumping parameters. The time delays are assumed to be dependent on the system modes. Delay-dependent conditions for the solvability of these problems are obtained via parameter-dependent Lyapunov functionals. Furthermore, it is shown that the desired state feedback controller can be designed by solving a set of linear matrix inequalities. Finally, the simulation is provided to demonstrate the effectiveness of the proposed methods.
基金Sponsored by the Scientific and Technical Research Project Foundation of Education Department of Heilongjiang Province(Grant No. 10551013).
文摘This paper investigates the problem of robust L1 model reduction for continuous-time uncertain stochastic time-delay systems. For a given mean-square stable system, our purpose is to construct reduced-order systems, such that the error system between these two models is mean-square asymptotically stable and has a guaranteed L1 (also called peak-to-peak) performance. The peak-to-peak gain criterion is first established for stochastic time-delay systems, and the corresponding model reduction problem is solved by using projection lemma. Sufficient conditions are obtained for the existence of admissible reduced-order models in terms of linear matrix inequalities (LMIs) plus matrix inverse constraints. Since these obtained conditions are not expressed as strict LMIs, the cone complementarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints, which can be readily solved by standard numerical software. In addition, the development of reduced-order models with special structures, such as the delay-free model, is also presented. The efficiency of the proposed methods is demonstrated via a numerical example.
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.
基金Supported by NSFC(Nos.10671182,12061020)NSF of Guizhou Province(Nos.QKH[2019]1123,QKHKY[2021]088,QKHKY[2022]301,QKH-ZK[2021]331)the Ph.D.Project of Guizhou Education University(No.2021BS005)。
文摘A stochastic stage-structure predator-prey system with impulsive effect is investigated.First,we build the corresponding system without impulse in order to demonstrate the existence and uniqueness of the global positive solution.Second,by selecting an appropriate Lyapunov function,we provide the sufficient condition for the existence of a positive T-periodic solution.Finally,numerical simulations illustrate our theoretical results,which show that the impulse or the white noises can result in the extinction of the predator in a certain condition.
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.
基金Partially supported by NSFC(No.11701304)the K.C.Wong Education Foundation。
文摘In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.
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.
文摘The heavy quarks present in the quark-gluon plasma(QGP)can act as a probe of relativistic heavy ion collisions as they retain the memory of their interaction history.In a previous study,a stochastic Schrödinger equation(SSE)has been applied to describe the evolution of heavy quarks,where an external field with random phases is used to simulate the thermal medium.In this work,we study the connection between the SSE and the Boltzmann transport equation(BE)approach in the Keldysh Green’s function formalism.By comparing the Green’s function of the heavy quark from the SSE and the Keldysh Green’s functions leading to the Boltzmann equation,we demonstrate that the SSE is consistent with the Boltzmann equation in the weak coupling limit.We subsequently confirm their consistency through numerical calculations.
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.
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.
基金the Deanship of Scientific Research at King Khalid University for funding this research through the Large Group Research Project under grant number RGP2/324/46.
文摘Intelligent Traffic Management(ITM)has progressively developed into a critical component of modern transportation networks,significantly enhancing traffic flow and reducing congestion in urban environments.This research proposes an enhanced framework that leverages Deep Q-Learning(DQL),Game Theory(GT),and Stochastic Optimization(SO)to tackle the complex dynamics in transportation networks.The DQL component utilizes the distribution of traffic conditions for epsilon-greedy policy formulation and action and choice reward calculation,ensuring resilient decision-making.GT models the interaction between vehicles and intersections through probabilistic distributions of various features to enhance performance.Results demonstrate that the proposed framework is a scalable solution for dynamic optimization in transportation networks.
