带Poisson跳和Markovian调制的中立型随机延迟微分方程的数值解的收敛性(英文)

Convergence of Numerical Solutions to Neutral Stochastic Delay Differential Equation with Poisson Jump and Markovian Switching

本文研究带Poisson跳和Markovian调制的中立型随机微分方程的数值解的收敛性质.用数值逼近方法求此微分方程的解,并证明了Euler近似解在此线性增长条件和全局Lipschitz条件更弱的条件下仍均方收敛于此方程的解析解.

The main purpose of this paper is to study the convergence of numerical solutions to a class of neutral stochastic delay differential equations with Poisson jump and Markovian switching.A numerical approximation scheme is proposed to approximate the solutions to neutral stochastic delay differential equations with Poisson jump and Markovian switching.It is proved that the Euler approximation solutions converge to the analytic solutions in the mean square under weaker conditions than the linear growth condit...