Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations
type: Item
instance of: scholarly article
title: Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations
zbMATH Open document ID: 1121.60071
author: Evelyn Buckwar
author: Rózsa Horváth-Bokor
author: Renate Winkler
published in: BIT
publication date: 2006-09-12T00:00:00Z
review text: The authors consider drift-implicit two-step schemes of the form \[ \begin{aligned}\alpha_2 X_{i+1}+ \alpha_1 X_i+ \alpha_0 X_{i-1} &= h[\beta_2 f(t_{i+1}, X_{i+1})+ \beta_1 f(t_i, X_i)+ \beta_0 f(t_{i-1}, X_{i-1})]\\ &\quad +\gamma_1 G(t_i, X_i)\Delta W_i+ \gamma_0 G(t_{i-1}, X_{i-1})\Delta W_{i-1}\end{aligned} \] with given initial values \(X_0\), \(X_1\) for the system of SDEs \[ dX(t)= f(t, X(t))\,dt+ G(t, X(t))\,dW(t). \] They investigate when the numerical scheme shares asymptotic properties of the system choosing as a test equation the linear scalar SDE \[ dX(t)=\lambda X(t)\,dt+\mu X(t)\,dW(t) \] with complex coefficients \(\lambda\), \(\mu\).
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 5053136
reviewed by: Grigori N. Milstein
MaRDI profile type: Publication
full work available at URL: s10543-006-0060-5
OpenAlex ID: W2096710166
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DOI: 10.1007/S10543-006-0060-5
description: scientific article