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

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.