Stability of numerical methods for solving stochastic differential equations
type: Item
instance of: scholarly article
title: Stability of numerical methods for solving stochastic differential equations
zbMATH Open document ID: 0852.65145
DOI: 10.1007/BF02104707
author: S. S. Artem'ev
published in: Siberian Mathematical Journal
publication date: 1996-08-14T00:00:00Z
review text: Use of numerical methods of solving stochastic differential equations (SDE) for statistically modeling the dynamics of various stochastic objects often encounters the problem of instability of a numerical solution; this fact stimulates further development of stability theory for these methods. The primary attention of the present article focuses on the question of mean square stability of numerical methods for solving SDE. Also, a definition is exhibited for a system stiff in mean square, verification of whose conditions in practice causes no difficulties. As numerical methods to be studied, we take the Rosenbrock-type generalized methods. We obtain a sufficient condition for mean square stability of numerical methods in their application to linear mean square asymptotically stable SDE systems with multiplicative noise. We bring an example of a mean square \(A\)-stable numerical method for solving the SDE systems in the sense of Itô and study mean square stability for known numerical methods of solving SDE.
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 917129
zbMATH Keywords: \(A\)-stability
zbMATH Keywords: stiff systems
zbMATH Keywords: Rosenbrock methods
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: mean square stability
MaRDI profile type: Publication
cites work: A special stability problem for linear multistep methods
cites work: On the exponential stability and instability of linear stochastic systems
cites work: Q4004325
full work available at URL: https://doi.org/10.1007/bf02104707
OpenAlex ID: W2089408984
description: scientific article; zbMATH DE number 917129