怀化学院学报
懷化學院學報
부화학원학보
JOURNAL OF HUAIHUA TEACHERS COLLEGE
2012年
5期
1-6
,共6页
半隐Milstein方法%随机微分方程%均方稳定%渐近稳定
半隱Milstein方法%隨機微分方程%均方穩定%漸近穩定
반은Milstein방법%수궤미분방정%균방은정%점근은정
semi- implicit Milstein methods%stochastic differential equations%mean square stability%asymptoticstability
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△≠〉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．
研究瞭隨機微分方程改進的半隱Milstein方法的均方穩定和漸近穩定性．對線性檢驗方程，得到瞭改進的半隱Milstein方法對任意步長△≠〉0均方穩定的充要條件是3/4 ≤ θ ≤ 1．證明瞭噹方法的步長充分小時，方法能保持原繫統的漸近穩定性．
연구료수궤미분방정개진적반은Milstein방법적균방은정화점근은정성．대선성검험방정，득도료개진적반은Milstein방법대임의보장△≠〉0균방은정적충요조건시3/4 ≤ θ ≤ 1．증명료당방법적보장충분소시，방법능보지원계통적점근은정성．
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.
