Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay
type: Item
instance of: scholarly article
title: Existence and uniqueness of solutions to neutral stochastic functional differential equations with infinite delay
zbMATH Open document ID: 1195.34123
published in: Applied Mathematics and Computation
publication date: 2009-12-16T00:00:00Z
review text: The authors prove an existence and uniqueness result for a neutral stochastic delay differential equation with unbounded delay driven by Brownian motion with initial condition in the state space of bounded continuous functions on \((-\infty,0]\) taking values in \({\mathbb R}^d\). Their basic assumption is a local Lipschitz and a linear growth condition on the coefficients with respect to the supremum norm on the state space. The existence proof is based on the usual successive approximation procedure.
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 34K05
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5648684
zbMATH Keywords: neutral stochastic functional differential equations
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: infinite delay
author: Haibo Bao
author: Jinde Cao
reviewed by: Michael Scheutzow
MaRDI profile type: Publication
full work available at URL: j.amc.2009.07.025
OpenAlex ID: W2055775664
cites work: Q4369402
cites work: Q4086525
cites work: Introduction to functional differential equations
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cites work: On the exponential stability in mean square of neutral stochastic functional differential equations
cites work: Exponential stability in mean square of neutral stochastic differential functional equations
cites work: New criteria on exponential stability of neutral stochastic differential delay equations
cites work: Q4767195
cites work: Stability of functional differential equations
DOI: 10.1016/J.AMC.2009.07.025
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description: scientific article; zbMATH DE number 5648684