Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations
type: Item
instance of: scholarly article
title: Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations
zbMATH Open document ID: 1391.65025
author: Chao Yue
published in: Science China. Mathematics
publication date: 2018-04-04T00:00:00Z
review text: For test equations that are Itô stochastic differential equations (SDE) of the form \(dx(t)= \alpha x(t)dt+\mu x(t)dW(t)\) (where \(\alpha\), \(\mu\) are constants) whose mean-square stability is known, a theorem is proved that specifies step-sizes for which the author's improved split-step theta method (ISST) is mean-square stable when applied to these test equations. Conditions are identified and proved under which ISST is exponentially mean-square stable when applied to nonautonomous systems of SDE of the form \(dx(t)= f (t,x(t))dt+ g(t, x(t)) dW(t)\). Numerical results for two examples are given that demonstrate the accuracy of the theorems.
reviewed by: Melvin D. Lax
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
zbMATH DE Number: 6855826
zbMATH Keywords: stochastic differential equations
zbMATH Keywords: mean-square stability
zbMATH Keywords: improved split-step theta methods
zbMATH Keywords: exponential mean-square stability
Wikidata QID: Q115602261
MaRDI profile type: Publication
full work available at URL: s11425-016-0132-2
OpenAlex ID: W2565040976
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DOI: 10.1007/S11425-016-0132-2
description: scientific article; zbMATH DE number 6855826