Second-order neutral stochastic evolution equations with heredity
type: Item
instance of: scholarly article
title: Second-order neutral stochastic evolution equations with heredity
zbMATH Open document ID: 1077.34062
DOI: 10.1155/S1048953304309020
author: Mark McKibben
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 2005-05-09T00:00:00Z
full work available at URL: https://eudml.org/doc/51875
review text: The author considers an abstract neutral semilinear stochastic evolution equation of the form \[ d(X'(t)-f_1(t,X_t)) =AX(t)dt+f_2(t,X_t)dt+g(t,X_t)dW(t). \] Here, \(A\) generates a strongly continuous cosine family of operators on a Hilbert space, \(W\) is an infinite-dimensional Wiener process and \(X_t\) denotes the solution segment at time \(t\). Various results for this equation are derived. First, existence and uniqueness of a mild solution is established under Lipschitz conditions. Then, continuous dependenc on the initial segment as well as moment estimates are treated. Finally, the existence and uniqueness result is generalized to the case of Carathéodory conditions. The paper closes with an example discussing an initial-boundary value problem.
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34K50
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 2166664
zbMATH Keywords: stochastic evolution equation with delay
zbMATH Keywords: semilinear equation
zbMATH Keywords: strongly continuous cosine family
reviewed by: Markus Reiß
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2166664