This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
In this work,we investigate the existence and asymptotic stability in mean square of mild solutions for non-linear impulsive neutral stochastic evolution equations with infinite delays in distribution in a real separa...In this work,we investigate the existence and asymptotic stability in mean square of mild solutions for non-linear impulsive neutral stochastic evolution equations with infinite delays in distribution in a real separable Hilbert space.By using the Banach fixed point principle,some sufficient conditions are derived to ensure the asymptotic stability of mild solutions.Moreover,we investigate the Hyers-Ulam stability for such stochastic system.Finally,an illustrative example is given to demonstrate the effectiveness of the obtained results.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 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
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金supported by the Excellent Talents Support Program for Colleges and Universities in Anhui Province(Grant No.gxyqZD2020003)。
文摘In this work,we investigate the existence and asymptotic stability in mean square of mild solutions for non-linear impulsive neutral stochastic evolution equations with infinite delays in distribution in a real separable Hilbert space.By using the Banach fixed point principle,some sufficient conditions are derived to ensure the asymptotic stability of mild solutions.Moreover,we investigate the Hyers-Ulam stability for such stochastic system.Finally,an illustrative example is given to demonstrate the effectiveness of the obtained results.
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 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.
