随机微分方程改进半隐Milstein方法的稳定性(英文)  

Stability of Improved Semi-implicit Milstein Methods for Stochastic Differential Equations

作　　者：李启勇[1] 

机构地区：[1]怀化学院数学系,湖南怀化418008

出　　处：《怀化学院学报》2012年第5期1-6,共6页Journal of Huaihua University

基　　金：湖南省教育厅青年项目(11B095)

摘　　要：研究了随机微分方程改进的半隐Milstein方法的均方稳定和渐近稳定性.对线性检验方程,得到了改进的半隐Milstein方法对任意步长Δt>0均方稳定的充要条件是3/4≤θ≤1.证明了当方法的步长充分小时,方法能保持原系统的渐近稳定性.This paper gives investigation of mean - square and asymptotic stability of improved semi - implicit Milstein methods for stochastic differential equations. It is shown that the improved semi - implicit Milstein methods recovered the mean- square stability properties of the linear test equation, if and only if 3/4 ≤ θ ≤ 1. For asymptotic stability, we proved that the methods can reproduce the stability of the test problem provided that the stepsize is sufficiently small.

关 键 词：半隐Milstein方法 随机微分方程 均方稳定 渐近稳定 

分 类 号：O211.63[理学—概率论与数理统计]