随机发展时滞方程的Khasminskii型定理和LaSalle-Type定理

Strong convergence rates of modified truncated EM methods for neutral stochastic differential delay equations

The aim of this paper is to investigate strong convergence of modified truncated Euler-Maruyama method for neutral stochastic differential delay equations introduced in Lan (2018). Strong convergence rates of the given numerical scheme to the exact solutions at fixed time $T$ are obtained under local Lipschitz and Khasminskii-type conditions. Moreover, convergence rates over a time interval $[0,T]$ are also obtained under additional polynomial growth condition on $g$ without the weak monotonicity condition (which is usually the standard assumption to obtain the convergence rate). Two examples …

Strong convergence rate of the truncated Euler-Maruyama method for stochastic differential delay equations with Poisson jumps

In this paper, we study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are investigated under the generalized Khasminskii-type condition.

随机延迟微分方程数值方法的均方指数稳定性

Mean square exponential stability of numerical methods for stochastic differential delay equations

本文研究随机延迟微分方程的θ-EM和MTEM数值方法的均方指数稳定性，提出新判据，并用两个例子验证。

The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations

This paper focuses on explicit approximations for nonlinear stochastic delay differential equations (SDDEs). Under the weakly local Lipschitz and some suitable conditions, a generic truncated Euler-Maruyama (TEM) scheme for SDDEs is proposed, which numerical solutions are bounded and converge to the exact solutions in qth moment for q>0. Furthermore, the 1/2 order convergent rate is yielded. Under the Khasminskii-type condition, a more precise TEM scheme is given, which numerical solutions are exponential stable in mean square and P-1. Finally, several numerical experiments are carried out to …

无限时域下带非线性扩散项的随机延迟微分方程的隐式数值逼近

Implicit numerical approximation for stochastic delay differential equations with the nonlinear diffusion term in the infinite horizon

本文在无限时域广义单调性等条件下，用后向Euler-Maruyama方法逼近带非线性扩散的随机延迟微分方程，证明其无限时域强收敛阶为1/2、分段过程测度收敛于原不变测度，并通过仿真验证理论结果。