Stochastic Volterra equations in weighted spaces
type: Item
instance of: scholarly article
title: Stochastic Volterra equations in weighted spaces
zbMATH Open document ID: 1197.60065
DOI: 10.1216/JIE-2010-22-1-1
author: John A. D. Appleby
author: M. Riedle
published in: Journal of Integral Equations and Applications
publication date: 2010-05-26T00:00:00Z
review text: The authors consider the asymptotic stability and decay rates (in various modes of convergence) of solutions to stochastically perturbed Volterra equations to the equilibrium solution of a related unperturbed deterministic Volterra equation. In particular it is shown that when the measure and state-independent diffusion coefficient of a linear Itô-Volterra equation lie in appropriate \(L^p\)-weighted spaces, the solution also lies in such a space in both a moment and an almost sure sense.
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 5712444
zbMATH Keywords: stochastic Volterra equations
zbMATH Keywords: stochastic functional differential equations
zbMATH Keywords: stability
zbMATH Keywords: weighted spaces
reviewed by: Andrew Dale
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5712444