Numerical solutions of stochastic differential delay equations under local Lipschitz condition
type: Item
instance of: scholarly article
title: Numerical solutions of stochastic differential delay equations under local Lipschitz condition
zbMATH Open document ID: 1015.65002
DOI: 10.1016/S0377-0427(02)00750-1
author: Xuerong Mao
author: Sotirios Sabanis
published in: Journal of Computational and Applied Mathematics
publication date: 2003-03-16T00:00:00Z
review text: Under certain hypotheses, which include the less restrictive assumption that \(f,g\) satisfy a local (rather than global) Lipschitz condition, a theorem is proved establishing convergence of Euler-Maruyama approximate solutions to the solution of the stochastic differential delay equation with variable delay \[ dx(t)= f\biggl(x,\bigl( \delta(t)\bigr)\biggr) dt+g\biggl(x(t), x \bigl(\delta(t) \bigr)\biggr) dB(t) \] where \(B\) is an \(m\)-dimensional Brownian motion.
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
zbMATH DE Number: 1882249
zbMATH Keywords: stochastic differential delay equations
zbMATH Keywords: local Lipschitz condition
zbMATH Keywords: Euler-Maruyama method
zbMATH Keywords: convergence
zbMATH Keywords: Brownian motion
reviewed by: Melvin D. Lax
MaRDI profile type: Publication
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full work available at URL: s0377-0427(02)00750-1
OpenAlex ID: W2140333923
description: scientific article; zbMATH DE number 1882249