In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocal...In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species.We prove that the traveling wavefronts are exponentially stable,when the initial perturbation around the traveling waves decays exponentially as x→-∞,but in other locations,the initial data can be arbitrarily large.The adopted methods are the weighted energy with the comparison principle and squeezing technique.展开更多
A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where ...A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.展开更多
The paper proposes a new method to estimate nonlinear diffusions based on discretely observed data, and gives some properties of the corresponding parameters estimation.
Necessary conditions are proved for certain problems of optimal control of diffusions where hard end constraints occur. The main results apply to several dimensional problems, where some of the state equations involve...Necessary conditions are proved for certain problems of optimal control of diffusions where hard end constraints occur. The main results apply to several dimensional problems, where some of the state equations involve Brownian motions, but not the equations corresponding to states being hard restricted at the terminal time. The necessary conditions are stated in terms of weak variations. Two versions of necessary conditions are given, one version involving solutions of variational equations, the other one involving first order adjoint equations.展开更多
Treats of dynamical systems with finite number of degrees of freedom such that the time evolution of the configuration variables for given initial conditions can well be described by controlled diffusions.Two suitable...Treats of dynamical systems with finite number of degrees of freedom such that the time evolution of the configuration variables for given initial conditions can well be described by controlled diffusions.Two suitable forms of stochastic action associated with the controlled diffusions are introduced in the general framework of stochastic control theory.By discretizing the stochastic action,the dynamical equations for the controlled diffusions of the given systems are derived in terms of generalized coordinates.These equations,together with the continuity equation,describe exactly the probability approach of the diffusion motion.展开更多
First-principles calculations based on density functional theory are used to investigate the adsorptions and diffusions of carbon atoms on the surface and in the subsurface of Co （200）. The preferred site for the ca...First-principles calculations based on density functional theory are used to investigate the adsorptions and diffusions of carbon atoms on the surface and in the subsurface of Co （200）. The preferred site for the carbon atom on the surface is the hollow site, and the preferred site in the subsurface is the octahedral site. There is charge transfer from the surface to the adsorbed carbon atom, and for the most favorable adsorbed structure the charge transfer is largest. Moreover, the energy barriers for the diffusions of carbon atoms on the surface and from the surface into the subsurface and then back to the surface are calculated in detail. The results indicate that the energy barrier for the diffusion of carbon atoms on the surface is comparable to that from the subsurface to the surface. The results imply that both the direct surface nucleation and the surface segregation from Co bulk can be observed in the chemical vapor deposition growth of graphene on Co （200） substrate, which can gain a new insight into the growth mechanism of graphene.展开更多
In this paper, the stabilities of boundary equilibrium and positive equilibrium of two_species Ayala competitive systems with two different diffusions are discussed, and dynamic behaviors of species are obtained. At t...In this paper, the stabilities of boundary equilibrium and positive equilibrium of two_species Ayala competitive systems with two different diffusions are discussed, and dynamic behaviors of species are obtained. At the same time, the dynamic behaviors between systems with diffusion and those without diffusion are compared. This shows the influence of diffusions on the persistence of species.展开更多
This work is devoted to practical stability of a class of regime-switching diffusions. First, the notion of practical stability is introduced. Then, sufficient conditions for practical stability and practical instabil...This work is devoted to practical stability of a class of regime-switching diffusions. First, the notion of practical stability is introduced. Then, sufficient conditions for practical stability and practical instability in probability and in pth mean are provided using a Lyapunov function argument. In addition, easily verifiable conditions on drift and diffusion coefficients are also given. Moreover, examples are supplied for demonstration purposes.展开更多
Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio' s semigroup for such optimal control problems was constructed. A Hamil...Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio' s semigroup for such optimal control problems was constructed. A Hamilton-Jacobi-Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function was such optimal control problems is shown to be a viscosity solution of this equation.展开更多
Consistency and asymptotic normality of the sieve estimator and an approximate maximum likelihood estimator of the drift coefficient of an interacting particles of diffusions are studied. For the sieve estimator, obse...Consistency and asymptotic normality of the sieve estimator and an approximate maximum likelihood estimator of the drift coefficient of an interacting particles of diffusions are studied. For the sieve estimator, observations are taken on a fixed time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the dimension of the sieve. For the approximate maximum likelihood estimator, discrete observations are taken in a time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the number of observation time points.展开更多
Stock price volatility is considered the main matter of concern within the investment grounds.However,the diffusivity of these prices should as well be considered.As such,proper modelling should be done for investors ...Stock price volatility is considered the main matter of concern within the investment grounds.However,the diffusivity of these prices should as well be considered.As such,proper modelling should be done for investors to stay healthy-informed.This paper suggest to model stock price diffusions using the heat equation from physics.We hypothetically state that,our model captures and model the diffusion bubbles of stock prices with a better precision of reality.We compared our model with the standard geometric Brownian motion model which is the wide commonly used stochastic differential equation in asset valuation.Interestingly,the models proved to agree as evidenced by a bijective relation between the volatility coefficients of the Brownian motion model and the diffusion coefficients of our heat diffusion model as well as the corresponding drift components.Consequently,a short proof for the martingale of our model is done which happen to hold.展开更多
In this paper,we study the inverse local times at 0 of one-dimensional reflected diffusions on[0,∞)and establish a comparison principle for these inverse local times.We also provide applications to Green function est...In this paper,we study the inverse local times at 0 of one-dimensional reflected diffusions on[0,∞)and establish a comparison principle for these inverse local times.We also provide applications to Green function estimates for non-local operators.展开更多
Using the method of Girsanov transformation,we establish the Talagrand’s T_(2)-inequality for diffusion on the path space C([0,N],Rd)with respect to a uniform metric,with the constant independent of N.This improves t...Using the method of Girsanov transformation,we establish the Talagrand’s T_(2)-inequality for diffusion on the path space C([0,N],Rd)with respect to a uniform metric,with the constant independent of N.This improves the known results for the L 2-metric.展开更多
Our interest here in this investigation is to explore the thermophoresis and Brownian motion characteristics in flow induced by stretched surface.Electrically conducted Jeffrey material formulates the flow equation.Li...Our interest here in this investigation is to explore the thermophoresis and Brownian motion characteristics in flow induced by stretched surface.Electrically conducted Jeffrey material formulates the flow equation.Linear forms of stretching and free stream velocities are imposed.Nonlinear radiation and convective heating processes describe the phenomenon of heat transfer.Passive controls of nanoparticles are considered on the boundary.The compatible transformations produce the strong nonlinear differential systems.The problems are computed analytically utilizing HAM.Converge nee domain is detennined and major results are concluded for different parameters involved.Heat transfer rate and drag force are also explained for various physical variables.Our analysis reveals that heat transfer rate augments via larger radiation parameter and Biot number.Moreover larger Brownian motion and thermophoresis parameters have opposite characteristics on concentration field.展开更多
For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The ...For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.展开更多
Cerebral small vessel disease encompasses a group of neurological disorders characterized by injury to small blood vessels,often leading to stroke and dementia.Due to its diverse etiologies and complex pathological me...Cerebral small vessel disease encompasses a group of neurological disorders characterized by injury to small blood vessels,often leading to stroke and dementia.Due to its diverse etiologies and complex pathological mechanisms,preventing and treating cerebral small vessel vasculopathy is challenging.Recent studies have shown that the glymphatic system plays a crucial role in interstitial solute clearance and the maintenance of brain homeostasis.Increasing evidence also suggests that dysfunction in glymphatic clearance is a key factor in the progression of cerebral small vessel disease.This review begins with a comprehensive introduction to the structure,function,and driving factors of the glymphatic system,highlighting its essential role in brain waste clearance.Afterwards,cerebral small vessel disease was reviewed from the perspective of the glymphatic system,after which the mechanisms underlying their correlation were summarized.Glymphatic dysfunction may lead to the accumulation of metabolic waste in the brain,thereby exacerbating the pathological processes associated with cerebral small vessel disease.The review also discussed the direct evidence of glymphatic dysfunction in patients and animal models exhibiting two subtypes of cerebral small vessel disease:arteriolosclerosis-related cerebral small vessel disease and amyloid-related cerebral small vessel disease.Diffusion tensor image analysis along the perivascular space is an important non-invasive tool for assessing the clearance function of the glymphatic system.However,the effectiveness of its parameters needs to be enhanced.Among various nervous system diseases,including cerebral small vessel disease,glymphatic failure may be a common final pathway toward dementia.Overall,this review summarizes prevention and treatment strategies that target glymphatic drainage and will offer valuable insight for developing novel treatments for cerebral small vessel disease.展开更多
This paper studies the unsteady heat and mass natural convection in a highly porous medium bounded by an infinite vertical porous wall. The unsteady source of the problem arises from the transverse oscillations in suc...This paper studies the unsteady heat and mass natural convection in a highly porous medium bounded by an infinite vertical porous wall. The unsteady source of the problem arises from the transverse oscillations in suction velocity of fluids, The analytical results for the problem are obtained based on the method of small parameter, and show that the natural circulation in the porous medium is affected by this kind of oscillation.展开更多
Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion u...Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion until it first exits D, at which time it stays at the exit point ξ for an independent exponential holding time with rate βξ and then leaves ξ by a jump into D according to the distribution ξ. Once the process jumps inside, it starts the diffusion afresh. The same evolution is repeated independently each time the process jumped into the domain. The resulting Markov process is called diffusion with holding and jumping boundary （DHJ）, which is not reversible due to the jumping. In this paper we provide a study of DHJ on its generator, stationary distribution and the speed of convergence.展开更多
We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),...We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.展开更多
We investigate a class of ecological models with local-nonlocal diffusions and different free boundaries.This is PartⅠof a two-part series,in which the existence,uniqueness,regularity and estimates of global solution...We investigate a class of ecological models with local-nonlocal diffusions and different free boundaries.This is PartⅠof a two-part series,in which the existence,uniqueness,regularity and estimates of global solution is studied.The spreading-vanishing dichotomy,criteria governing spreading and vanishing,long-time behavior of solution and the estimation of the spreading speed when spreading happens will be studied in the separate PartⅡ.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12261081).
文摘In this paper,we are concerned with the stability of traveling wavefronts of a Belousov-Zhabotinsky model with mixed nonlocal and degenerate diffusions.Such a system can be used to study the competition among nonlocally diffusive species and degenerately diffusive species.We prove that the traveling wavefronts are exponentially stable,when the initial perturbation around the traveling waves decays exponentially as x→-∞,but in other locations,the initial data can be arbitrarily large.The adopted methods are the weighted energy with the comparison principle and squeezing technique.
基金supported by the National Basic Research Program of China (973 Program, 2007CB814904)the National Natural Science Foundations of China (10921101)+2 种基金Shandong Province (2008BS01024, ZR2010AQ004)the Science Funds for Distinguished Young Scholars of Shandong Province (JQ200801)Shandong University (2009JQ004),the Independent Innovation Foundations of Shandong University (IIFSDU,2009TS036, 2010TS060)
文摘A stochastic maximum principle for the risk-sensitive optimal control prob- lem of jump diffusion processes with an exponential-of-integral cost functional is derived assuming that the value function is smooth, where the diffusion and jump term may both depend on the control. The form of the maximum principle is similar to its risk-neutral counterpart. But the adjoint equations and the maximum condition heavily depend on the risk-sensitive parameter. As applications, a linear-quadratic risk-sensitive control problem is solved by using the maximum principle derived and explicit optimal control is obtained.
文摘The paper proposes a new method to estimate nonlinear diffusions based on discretely observed data, and gives some properties of the corresponding parameters estimation.
文摘Necessary conditions are proved for certain problems of optimal control of diffusions where hard end constraints occur. The main results apply to several dimensional problems, where some of the state equations involve Brownian motions, but not the equations corresponding to states being hard restricted at the terminal time. The necessary conditions are stated in terms of weak variations. Two versions of necessary conditions are given, one version involving solutions of variational equations, the other one involving first order adjoint equations.
文摘Treats of dynamical systems with finite number of degrees of freedom such that the time evolution of the configuration variables for given initial conditions can well be described by controlled diffusions.Two suitable forms of stochastic action associated with the controlled diffusions are introduced in the general framework of stochastic control theory.By discretizing the stochastic action,the dynamical equations for the controlled diffusions of the given systems are derived in terms of generalized coordinates.These equations,together with the continuity equation,describe exactly the probability approach of the diffusion motion.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51002014,51202017,and 51372095)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120061120039)+2 种基金the Funds from the Science and Technology Department of Jilin Province,China(Grant Nos.20120745 and 20130101029JC)the Funds from the Department of Education of Jilin Province,China(Grant No.2013279)the Youth Science Research Foundation of Liaoning University,China(Grant No.2013LDQN20)
文摘First-principles calculations based on density functional theory are used to investigate the adsorptions and diffusions of carbon atoms on the surface and in the subsurface of Co （200）. The preferred site for the carbon atom on the surface is the hollow site, and the preferred site in the subsurface is the octahedral site. There is charge transfer from the surface to the adsorbed carbon atom, and for the most favorable adsorbed structure the charge transfer is largest. Moreover, the energy barriers for the diffusions of carbon atoms on the surface and from the surface into the subsurface and then back to the surface are calculated in detail. The results indicate that the energy barrier for the diffusion of carbon atoms on the surface is comparable to that from the subsurface to the surface. The results imply that both the direct surface nucleation and the surface segregation from Co bulk can be observed in the chemical vapor deposition growth of graphene on Co （200） substrate, which can gain a new insight into the growth mechanism of graphene.
文摘In this paper, the stabilities of boundary equilibrium and positive equilibrium of two_species Ayala competitive systems with two different diffusions are discussed, and dynamic behaviors of species are obtained. At the same time, the dynamic behaviors between systems with diffusion and those without diffusion are compared. This shows the influence of diffusions on the persistence of species.
基金the National Science Foundation (No. DMS-0603287, No. CMS-0510655)the National Security Agency (No. MSPF-068-029)+3 种基金the National Natural Science Foundation of China (No. 60574069)Program for NCET,in part by the Key Project of Chinese Ministry of Education 104053and in part by theWayne State University Research Enhancement Programthe National Science Foundation (No.DMS-0304928, No. DMS-0624849)
文摘This work is devoted to practical stability of a class of regime-switching diffusions. First, the notion of practical stability is introduced. Then, sufficient conditions for practical stability and practical instability in probability and in pth mean are provided using a Lyapunov function argument. In addition, easily verifiable conditions on drift and diffusion coefficients are also given. Moreover, examples are supplied for demonstration purposes.
文摘Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio' s semigroup for such optimal control problems was constructed. A Hamilton-Jacobi-Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function was such optimal control problems is shown to be a viscosity solution of this equation.
文摘Consistency and asymptotic normality of the sieve estimator and an approximate maximum likelihood estimator of the drift coefficient of an interacting particles of diffusions are studied. For the sieve estimator, observations are taken on a fixed time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the dimension of the sieve. For the approximate maximum likelihood estimator, discrete observations are taken in a time interval [0,T] and asymptotics are studied as the number of interacting particles increases with the number of observation time points.
文摘Stock price volatility is considered the main matter of concern within the investment grounds.However,the diffusivity of these prices should as well be considered.As such,proper modelling should be done for investors to stay healthy-informed.This paper suggest to model stock price diffusions using the heat equation from physics.We hypothetically state that,our model captures and model the diffusion bubbles of stock prices with a better precision of reality.We compared our model with the standard geometric Brownian motion model which is the wide commonly used stochastic differential equation in asset valuation.Interestingly,the models proved to agree as evidenced by a bijective relation between the volatility coefficients of the Brownian motion model and the diffusion coefficients of our heat diffusion model as well as the corresponding drift components.Consequently,a short proof for the martingale of our model is done which happen to hold.
基金supported by Simons Foundation(Grant No.520542)supported by National Natural Science Foundation of China(Grant Nos.11801283 and 12171252)。
文摘In this paper,we study the inverse local times at 0 of one-dimensional reflected diffusions on[0,∞)and establish a comparison principle for these inverse local times.We also provide applications to Green function estimates for non-local operators.
文摘Using the method of Girsanov transformation,we establish the Talagrand’s T_(2)-inequality for diffusion on the path space C([0,N],Rd)with respect to a uniform metric,with the constant independent of N.This improves the known results for the L 2-metric.
文摘Our interest here in this investigation is to explore the thermophoresis and Brownian motion characteristics in flow induced by stretched surface.Electrically conducted Jeffrey material formulates the flow equation.Linear forms of stretching and free stream velocities are imposed.Nonlinear radiation and convective heating processes describe the phenomenon of heat transfer.Passive controls of nanoparticles are considered on the boundary.The compatible transformations produce the strong nonlinear differential systems.The problems are computed analytically utilizing HAM.Converge nee domain is detennined and major results are concluded for different parameters involved.Heat transfer rate and drag force are also explained for various physical variables.Our analysis reveals that heat transfer rate augments via larger radiation parameter and Biot number.Moreover larger Brownian motion and thermophoresis parameters have opposite characteristics on concentration field.
基金supported by the Simons Foundation (Grant No. 209206)a General Research Fund of the University of Kansas
文摘For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.
基金supported by the National Natural Science Foundation of China,No.82274304(to YH)the Major Clinical Study Projects of Shanghai Shenkang Hospital Development Center,No.SHDC2020CR2046B(to YH)Shanghai Municipal Health Commission Talent Plan,No.2022LJ010(to YH).
文摘Cerebral small vessel disease encompasses a group of neurological disorders characterized by injury to small blood vessels,often leading to stroke and dementia.Due to its diverse etiologies and complex pathological mechanisms,preventing and treating cerebral small vessel vasculopathy is challenging.Recent studies have shown that the glymphatic system plays a crucial role in interstitial solute clearance and the maintenance of brain homeostasis.Increasing evidence also suggests that dysfunction in glymphatic clearance is a key factor in the progression of cerebral small vessel disease.This review begins with a comprehensive introduction to the structure,function,and driving factors of the glymphatic system,highlighting its essential role in brain waste clearance.Afterwards,cerebral small vessel disease was reviewed from the perspective of the glymphatic system,after which the mechanisms underlying their correlation were summarized.Glymphatic dysfunction may lead to the accumulation of metabolic waste in the brain,thereby exacerbating the pathological processes associated with cerebral small vessel disease.The review also discussed the direct evidence of glymphatic dysfunction in patients and animal models exhibiting two subtypes of cerebral small vessel disease:arteriolosclerosis-related cerebral small vessel disease and amyloid-related cerebral small vessel disease.Diffusion tensor image analysis along the perivascular space is an important non-invasive tool for assessing the clearance function of the glymphatic system.However,the effectiveness of its parameters needs to be enhanced.Among various nervous system diseases,including cerebral small vessel disease,glymphatic failure may be a common final pathway toward dementia.Overall,this review summarizes prevention and treatment strategies that target glymphatic drainage and will offer valuable insight for developing novel treatments for cerebral small vessel disease.
文摘This paper studies the unsteady heat and mass natural convection in a highly porous medium bounded by an infinite vertical porous wall. The unsteady source of the problem arises from the transverse oscillations in suction velocity of fluids, The analytical results for the problem are obtained based on the method of small parameter, and show that the natural circulation in the porous medium is affected by this kind of oscillation.
基金supported by National Natural Science Foundation of China(Grant No.11101433)the Fundamental Research Funds for the Central South University(Grant No.2011QNZT105)+1 种基金Doctorial Dissertation Program of Hunan Province(Grant No.YB2011B009)US National Science Foundation (Grant Nos.AMC-SS-0706713,DMS-0805929,NSFC-6398100 and CAS-2008DP173182)
文摘Consider a family of probability measures {vξ} on a bounded open region D C Rd with a smooth boundary and a positive parameter set {βξ}, all indexed by ξ∈δD. For any starting point inside D, we run a diffusion until it first exits D, at which time it stays at the exit point ξ for an independent exponential holding time with rate βξ and then leaves ξ by a jump into D according to the distribution ξ. Once the process jumps inside, it starts the diffusion afresh. The same evolution is repeated independently each time the process jumped into the domain. The resulting Markov process is called diffusion with holding and jumping boundary （DHJ）, which is not reversible due to the jumping. In this paper we provide a study of DHJ on its generator, stationary distribution and the speed of convergence.
基金Partial funding in support of this work was provided by the Natural Sciences and Engineering Research Council of Canada(NSERC)the Department of Mathematics at the University of Oregon。
文摘We construct superprocesses with dependent spatial motion(SDSMs)in Euclidean spaces R^(d)with d≥1 and show that,even when they start at some unbounded initial positive Radon measure such as Lebesgue measure on R^(d),their local times exist when d≤3.A Tanaka formula of the local time is also derived.
基金Supported by NSFC Grants(Grant Nos.12171120,11971128)。
文摘We investigate a class of ecological models with local-nonlocal diffusions and different free boundaries.This is PartⅠof a two-part series,in which the existence,uniqueness,regularity and estimates of global solution is studied.The spreading-vanishing dichotomy,criteria governing spreading and vanishing,long-time behavior of solution and the estimation of the spreading speed when spreading happens will be studied in the separate PartⅡ.
