Successive approximations for solutions of stochastic integral equations of Volterra type
type: Item
instance of: scholarly article
title: Successive approximations for solutions of stochastic integral equations of Volterra type
zbMATH Open document ID: 0598.60064
DOI: 10.1016/0022-247X(84)90026-X
author: Constantin Tudor
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: The following Volterra stochastic equation \[ x(t)=\phi (t)\quad \sigma - r\leq t\leq \sigma \] \[ x(t)=\phi (t)+K_ 1(t)+\int^{t}_{\sigma}K_ 2(s,x_ s)dw(s)+\int^{t}_{\sigma}K_ 3(t,s,x_ s)ds\quad t\geq \sigma \] is considered in an abstract Wiener space (i,H,B), where w is a B-valued Wiener process. Under Caratheodory's conditions on the kernels \(K_ 2\), \(K_ 3\), the convergence in maximal quadratic mean of Picard's successive approximations to a solution of the above equation is proved.
Mathematics Subject Classification ID: 60H20
zbMATH DE Number: 3965120
zbMATH Keywords: Caratheodory's conditions
zbMATH Keywords: Picard's successive approximations
MaRDI profile type: Publication
cites work: Successive approximations for solutions of functional integral equations
cites work: Q3862194
cites work: Q3911172
description: scientific article; zbMATH DE number 3965120