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
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
We discuss stochastic functional partial differential equations and neutral partial differential equations of retarded type driven by fractional Brownian motion with Hurst parameter H 〉 1/2. Using the Girsanov transf...We discuss stochastic functional partial differential equations and neutral partial differential equations of retarded type driven by fractional Brownian motion with Hurst parameter H 〉 1/2. Using the Girsanov transformation argument, we establish the quadratic transportation inequalities for the law of the mild solution of those equations driven by fractional Brownian motion under the L2 metric and the uniform metric.展开更多
In the literature (Tan and Wang, 2010), Tan and Wang investigated the convergence of the split-step backward Euler (SSBE) method for linear stochastic delay integro-differential equations (SDIDEs) and proved the...In the literature (Tan and Wang, 2010), Tan and Wang investigated the convergence of the split-step backward Euler (SSBE) method for linear stochastic delay integro-differential equations (SDIDEs) and proved the mean-square stability of SSBE method under some condition. Unfortu- nately, the main result of stability derived by the condition is somewhat restrictive to be applied for practical application. This paper improves the corresponding results. The authors not only prove the mean-square stability of the numerical method but also prove the general mean-square stability of the numerical method. Furthermore, an example is given to illustrate the theory.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
In this paper we study the controllability of linear and nonlinear stochastic fractional systems with bounded operator having distributed delay in control.The necessary and sufficient conditions for controllability of...In this paper we study the controllability of linear and nonlinear stochastic fractional systems with bounded operator having distributed delay in control.The necessary and sufficient conditions for controllability of the linear system is obtained.Also,the nonlinear system is shown controllable under the assumption that the corresponding linear system is controllable and using the Banach contraction principle.展开更多
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.
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.
基金Acknowledgements The authors would like to thank the referees for helpful suggestions which allowed them to improve the presentation of this paper. This work was supported in part by the National Natural Science Foundation of China (Grant No. 11271093) and the Science Research Project of Hubei Provincial Department Of Education (No. Q20141306).
文摘We discuss stochastic functional partial differential equations and neutral partial differential equations of retarded type driven by fractional Brownian motion with Hurst parameter H 〉 1/2. Using the Girsanov transformation argument, we establish the quadratic transportation inequalities for the law of the mild solution of those equations driven by fractional Brownian motion under the L2 metric and the uniform metric.
基金supported by the Fundamental Research Funds for the Central Universities under Grant No. 2012089:31541111213China Postdoctoral Science Foundation Funded Project under Grant No.2012M511615the State Key Program of National Natural Science of China under Grant No.61134012
文摘In the literature (Tan and Wang, 2010), Tan and Wang investigated the convergence of the split-step backward Euler (SSBE) method for linear stochastic delay integro-differential equations (SDIDEs) and proved the mean-square stability of SSBE method under some condition. Unfortu- nately, the main result of stability derived by the condition is somewhat restrictive to be applied for practical application. This paper improves the corresponding results. The authors not only prove the mean-square stability of the numerical method but also prove the general mean-square stability of the numerical method. Furthermore, an example is given to illustrate the theory.
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the University Grants Commission[grant number MANF-2015-17-TAM-50645]from the government of India。
文摘In this paper we study the controllability of linear and nonlinear stochastic fractional systems with bounded operator having distributed delay in control.The necessary and sufficient conditions for controllability of the linear system is obtained.Also,the nonlinear system is shown controllable under the assumption that the corresponding linear system is controllable and using the Banach contraction principle.