具有马尔可夫调制的随机微分方程数值解的收敛性(英文)

Convergence of Numerical Solutions to Stochastic Differential Equations with Markovian Switching

本文在无穷维Hilbert空间中研究了一类具有马尔可夫调制的随机微分方程(SDEwMSs).在一般情况下SDEwMSs没有解析解.因此合适的数值逼近法,例如欧拉法,就是在研究它们性质时所采用的重要工具.本文在较弱的条件下不仅证明了欧拉近似解收敛于SDEwMSs的精确解(分析解),而且给出了欧拉近似阶的界.

This paper studies a class of stochastic different equations with Markovian switching （SDEwMSs） in the infinite dimensional Hilbert space. In general SDEwMSs do not have explicit solutions. Appropriate numerical approximations, such as the Euler scheme, are therefore a vital tool in exploring their porperties. In this paper,it is proved that the Euler approximate solutions will converge to the exact solutions for SDEwMSs under weaker conditions. The bound to the order of the Euler approximation is also provided.