An application of Taylor series in the approximation of solutions to stochastic differential equations with time-dependent delay
type: Item
instance of: scholarly article
title: An application of Taylor series in the approximation of solutions to stochastic differential equations with time-dependent delay
zbMATH Open document ID: 1222.65013
author: M. Milosevic
author: Miljana Jovanović
published in: Journal of Computational and Applied Mathematics
publication date: 2011-07-08T00:00:00Z
review text: The authors propose an analytic approximation method for solving stochastic differential equations with time-dependent delay: \[ \begin{aligned} dx(t) & =f(x(t),x(t-\delta(t)),t)dt+f(x(t),x(t-\delta(t)),t)dw(t),\;t\in [ t_{0},T],\\ x(t_{0}) & =\{\xi(\theta),\;\theta\in[-\tau,0]\},\\ \delta & :\;[t_{0},T]\longrightarrow[0,\tau]. \end{aligned} \] The method is based on Taylor approximations of the coefficients \(f\) and \(g\). The authors consider the \(L^{p}\) convergence and the convergence with probability one of the approximate solutions.
reviewed by: Grigori N. Milstein
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 5918669
zbMATH Keywords: stochastic differential equations with time-dependent delay
zbMATH Keywords: Taylor approximation
zbMATH Keywords: \(L^{p}\) and almost sure convergence
MaRDI profile type: Publication
full work available at URL: j.cam.2011.04.009
OpenAlex ID: W2031326290
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DOI: 10.1016/J.CAM.2011.04.009
description: scientific article; zbMATH DE number 5918669