On the stability of some second order numerical methods for weak approximation of It么 SDEs

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• 作者：Amir Haghighi (1) a.haghighi@modares.ac.ir
  S. Mohammad Hosseini (1) hossei_m@modares.ac.ir
• 关键词：Stochastic differential equations &#8211 ; Stochastic stability &#8211 ; Asymptotic stability &#8211 ; MS ; stability &#8211 ; Weak convergence &#8211 ; Predictor ; corrector methods
• 刊名：Numerical Algorithms
• 出版时间：May 2011
• 出版年：2011
• 期刊代码：48_10171398
• 类别：mt
• 卷：57
• 期：1
• 页码：101-124
• 数据来源：sp

摘要

In this paper, we first investigate the stability of two weak second order methods introduced by Debrabant and R枚脽ler (Appl Numer Math 59:582–594, 2009) and Platen (Math Comput Simulation 38:69–76, 1995). We then propose a new weak second order predictor-corrector method, with an improved stability properties, based on the R枚脽ler’s method as the predictor and the implicit method of Platen as the corrector. The stability functions of these methods, applied to a scalar linear test equation with multiplicative noise, are determined and their regions of stability are then compared with the corresponding stability regions of the test equation. Furthermore, we also investigate mean square stability (MS-stability) of these methods applied to a linear It么 2-dimensional stochastic differential test equation. Numerical examples will be presented to support the theoretical results.