In this paper,we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ∈(1/2,1) in a Hilbert space.We employ the α-norm in order to ...In this paper,we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ∈(1/2,1) in a Hilbert space.We employ the α-norm in order to reflect the relationship between H and the fractional power α.Sufficient conditions are established by using stochastic analysis theory and operator theory.An example is provided to illustrate the effectiveness of the proposed result.展开更多
We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approxi...Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.展开更多
This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to t...This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to the stochastic case.展开更多
In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on...In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on dual multi-Hilbertian spaces.展开更多
In this paper, we will consider following initial value problem of semilinear stochastic evolution equation in Hilbert Space: [GRAPHICS] where W(t) is a wiener process in H, H and Y are two real separable Hilbert Spac...In this paper, we will consider following initial value problem of semilinear stochastic evolution equation in Hilbert Space: [GRAPHICS] where W(t) is a wiener process in H, H and Y are two real separable Hilbert Spaces, A is an infinitesimal generator of a strongly continuous semigroup s(t) on Y, f(t, y): [0, T] x Y --> Y, and G(t, y): [0, T] X Y --> L(H, Y), y0: OMEGA --> Y is a ramdom variable of square integrable. We apply theory of the semigroup and obtain two conclusions of uniqueness of the mild solution of (1) which include the corresponding results in [4].展开更多
An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to...An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.展开更多
For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined b...For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.展开更多
This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear functional integro-differential stochastic evolution equations in real separable Hilbert spaces. Under some suitable a...This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear functional integro-differential stochastic evolution equations in real separable Hilbert spaces. Under some suitable assumptions, the existence, uniqueness and asymptotic stability of the square-mean almost automorphic mild solution to some stochastic differential equations are established. As an application, we analyze the almost automorphic mild solution to some stochastic partial functional differential equation which turns out to be in good agreement with our abstract results.展开更多
In this paper, we establish existence and uniqueness of the mild solutions to a class of neutral stochastic evolution equations driven by Poisson random measures in some Hilbert space. Moreover, we adopt the Faedo-Gal...In this paper, we establish existence and uniqueness of the mild solutions to a class of neutral stochastic evolution equations driven by Poisson random measures in some Hilbert space. Moreover, we adopt the Faedo-Galerkin scheme to approximate the solutions.展开更多
This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so...This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called "Acquistapace–Terreni" conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.展开更多
This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the ...This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.展开更多
In this paper, in the sense of the definition of almost periodicity given by H.Bohr using fixed-point principle, we investigate the existence and uniqueness of quadratic mean almost periodic solutions to semi-linear s...In this paper, in the sense of the definition of almost periodicity given by H.Bohr using fixed-point principle, we investigate the existence and uniqueness of quadratic mean almost periodic solutions to semi-linear stochastic integro-differential evolution equations associated with abstract Volterra equations. Some examples are also given to illustrate our theory.展开更多
This paper extends exit theorems of Da Prato and Zabczyk to nonconstant diffusion coefficients.It uses extensively general, exponential estimates due to Peszat.
We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on the functional space of such processes like completeness and composi...We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on the functional space of such processes like completeness and composition theorems. Under some conditions, we establish the existence, uniqueness, and the global exponentially stability of μ-pseudo almost automorphic mild solutions for a class of nonlinear stochastic evolution equations driven by Brownian motion in a separable Hilbert space.展开更多
In this paper,the numerical methods for semi-linear stochastic delay integro-difFerential equations are studied.The uniqueness,existence and stability of analytic solutions of semi-linear stochastic delay integro-diff...In this paper,the numerical methods for semi-linear stochastic delay integro-difFerential equations are studied.The uniqueness,existence and stability of analytic solutions of semi-linear stochastic delay integro-differential equations are studied and some suitable conditions for the mean-square stability of the analytic solutions are also obtained.Then the numerical approximation of exponential Euler method for semi-linear stochastic delay integro-differential equations is constructed and the convergence and the stability of the numerical method are studied.It is proved that the exponential Euler method is convergent with strong order 1/2 and can keep the mean-square exponential stability of the analytical solutions under some restrictions on the step size.In addition,numerical experiments are presented to confirm the theoretical results.展开更多
This paper mainly considers the optimal convergence analysis of the q-Maruyama method for stochastic Volterra integro-differential equations(SVIDEs)driven by Riemann-Liouville fractional Brownian motion under the glob...This paper mainly considers the optimal convergence analysis of the q-Maruyama method for stochastic Volterra integro-differential equations(SVIDEs)driven by Riemann-Liouville fractional Brownian motion under the global Lipschitz and linear growth conditions.Firstly,based on the contraction mapping principle,we prove the well-posedness of the analytical solutions of the SVIDEs.Secondly,we show that the q-Maruyama method for the SVIDEs can achieve strong first-order convergence.In particular,when the q-Maruyama method degenerates to the explicit Euler-Maruyama method,our result improves the conclusion that the convergence rate is H+1/2,H∈(0,1/2)by Yang et al.,J.Comput.Appl.Math.,383(2021),113156.Finally,the numerical experiment verifies our theoretical results.展开更多
The aim of this paper is to consider the convergence of the numerical methods for stochastic time-fractional evolution equations driven by fractional Brownian motion.The spatial and temporal regularity of the mild sol...The aim of this paper is to consider the convergence of the numerical methods for stochastic time-fractional evolution equations driven by fractional Brownian motion.The spatial and temporal regularity of the mild solution is given.The numerical scheme approximates the problem in space by the Galerkin finite element method and in time by the backward Euler convolution quadrature formula,and the noise by the L 2-projection.The strong convergence error estimates for both semi-discrete and fully discrete schemes are established.A numerical example is presented to verify our theoretical analysis.展开更多
基金supported by NSFC(11271020,11401010)Natural Science Foundation of Anhui Province(1308085QA14)+1 种基金supported by NSFC(11571071)Innovation Program of Shanghai Municipal Education Commission(12ZZ063)
文摘In this paper,we investigate the controllability for neutral stochastic evolution equations driven by fractional Brownian motion with Hurst parameter H ∈(1/2,1) in a Hilbert space.We employ the α-norm in order to reflect the relationship between H and the fractional power α.Sufficient conditions are established by using stochastic analysis theory and operator theory.An example is provided to illustrate the effectiveness of the proposed result.
文摘We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.
文摘Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.
基金Work supported by National Natural Science Foundation of China.
文摘This is the third part of the papers with the same title. We will discuss the problem of convergence of the semi-implicit difference scheme for a class of quasilinear SEE, which generalize the Crandall's work to the stochastic case.
文摘In this paper, nonstandard analysis is employed to present an existence theory of -valued stochastic differential equations involving evolution drift. And (C0, 1)-evolution systems are also defined and investigated on dual multi-Hilbertian spaces.
基金This work is supported by the National Science Foundation of China.
文摘In this paper, we will consider following initial value problem of semilinear stochastic evolution equation in Hilbert Space: [GRAPHICS] where W(t) is a wiener process in H, H and Y are two real separable Hilbert Spaces, A is an infinitesimal generator of a strongly continuous semigroup s(t) on Y, f(t, y): [0, T] x Y --> Y, and G(t, y): [0, T] X Y --> L(H, Y), y0: OMEGA --> Y is a ramdom variable of square integrable. We apply theory of the semigroup and obtain two conclusions of uniqueness of the mild solution of (1) which include the corresponding results in [4].
基金Supported by the National Natural Science Foundation of China(11101140,11301177)the China Postdoctoral Science Foundation(2011M500721,2012T50391)the Zhejiang Natural Science Foundation of China(Y6110775,Y6110789)
文摘An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.
文摘For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11201266 and 11171191)Tianyuan Youth Foundation of National Natural Science Foundation of China(Grant Nos.11026150 and 11026098)+2 种基金China Postdoctoral Science Foundation(Grant No.2013M541534)Shanghai Postdoctoral Science Foundation(Grant No.13R21415600)Excellent Youth Foundation of SDIBT
文摘This paper concerns the square-mean almost automorphic solutions to a class of abstract semilinear functional integro-differential stochastic evolution equations in real separable Hilbert spaces. Under some suitable assumptions, the existence, uniqueness and asymptotic stability of the square-mean almost automorphic mild solution to some stochastic differential equations are established. As an application, we analyze the almost automorphic mild solution to some stochastic partial functional differential equation which turns out to be in good agreement with our abstract results.
基金supported by the LPMC at Nankai University and National Natural Science Foundation of China(Grant No. 10671036)
文摘In this paper, we establish existence and uniqueness of the mild solutions to a class of neutral stochastic evolution equations driven by Poisson random measures in some Hilbert space. Moreover, we adopt the Faedo-Galerkin scheme to approximate the solutions.
基金Supported by National Natural Science Foundation of China(Grant Nos.11201266 and 11171191)TianyuanYouth Foundation of National Natural Science Foundation of China(Grant Nos.11026150 and 11026098)Excellent Youth Foundation of Shandong Institute of Business and Technology
文摘This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called "Acquistapace–Terreni" conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.
文摘This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.
文摘In this paper, in the sense of the definition of almost periodicity given by H.Bohr using fixed-point principle, we investigate the existence and uniqueness of quadratic mean almost periodic solutions to semi-linear stochastic integro-differential evolution equations associated with abstract Volterra equations. Some examples are also given to illustrate our theory.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 10171101, 79970120) a grant from Tsinghua University.
文摘This paper extends exit theorems of Da Prato and Zabczyk to nonconstant diffusion coefficients.It uses extensively general, exponential estimates due to Peszat.
基金the Natural Science Foundation of Anhui Province (1708085MA03)the National Natural Science Foundation of China (Grant Nos. 11401010, 11571071).
文摘We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on the functional space of such processes like completeness and composition theorems. Under some conditions, we establish the existence, uniqueness, and the global exponentially stability of μ-pseudo almost automorphic mild solutions for a class of nonlinear stochastic evolution equations driven by Brownian motion in a separable Hilbert space.
基金This research is supported by National Natural Science Foundation of China(Project No.11901173)by the Heilongjiang province Natural Science Foundation(LH2019A030)by the Heilongjiang province Innovation Talent Foundation(2018CX17).
文摘In this paper,the numerical methods for semi-linear stochastic delay integro-difFerential equations are studied.The uniqueness,existence and stability of analytic solutions of semi-linear stochastic delay integro-differential equations are studied and some suitable conditions for the mean-square stability of the analytic solutions are also obtained.Then the numerical approximation of exponential Euler method for semi-linear stochastic delay integro-differential equations is constructed and the convergence and the stability of the numerical method are studied.It is proved that the exponential Euler method is convergent with strong order 1/2 and can keep the mean-square exponential stability of the analytical solutions under some restrictions on the step size.In addition,numerical experiments are presented to confirm the theoretical results.
基金supported by the National Natural Science Foundation of China(No.12071403).
文摘This paper mainly considers the optimal convergence analysis of the q-Maruyama method for stochastic Volterra integro-differential equations(SVIDEs)driven by Riemann-Liouville fractional Brownian motion under the global Lipschitz and linear growth conditions.Firstly,based on the contraction mapping principle,we prove the well-posedness of the analytical solutions of the SVIDEs.Secondly,we show that the q-Maruyama method for the SVIDEs can achieve strong first-order convergence.In particular,when the q-Maruyama method degenerates to the explicit Euler-Maruyama method,our result improves the conclusion that the convergence rate is H+1/2,H∈(0,1/2)by Yang et al.,J.Comput.Appl.Math.,383(2021),113156.Finally,the numerical experiment verifies our theoretical results.
文摘The aim of this paper is to consider the convergence of the numerical methods for stochastic time-fractional evolution equations driven by fractional Brownian motion.The spatial and temporal regularity of the mild solution is given.The numerical scheme approximates the problem in space by the Galerkin finite element method and in time by the backward Euler convolution quadrature formula,and the noise by the L 2-projection.The strong convergence error estimates for both semi-discrete and fully discrete schemes are established.A numerical example is presented to verify our theoretical analysis.