Stochastic integration with respect to the cylindrical Wiener process via regularization
type: Item
instance of: scholarly article
zbMATH Open document ID: 1284.60112
DOI: 10.1142/S0219025713500240
author: Christian Olivera
published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics
publication date: 2013-11-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/1203.0279
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60H15
zbMATH DE Number: 6222498
zbMATH Keywords: stochastic calculus via regularization
zbMATH Keywords: Russo-Vallois integrals
zbMATH Keywords: cylindrical Wiener process
zbMATH Keywords: stochastic partial differential equation
MaRDI profile type: Publication
arXiv ID: 1203.0279
cites work: Hermite expansions and products of tempered distributions
cites work: Tempered generalized functions and Hermite expansions
cites work: ON STOCHASTIC GENERALIZED FUNCTIONS
cites work: Stochastic integrals for SPDEs: a comparison
cites work: Wiener chaos solutions of linear stochastic evolution equations
cites work: The Malliavin Calculus and Related Topics
cites work: Forward, backward and symmetric stochastic integration
cites work: The generalized covariation process and Itô formula
cites work: Ito formula for \(C^ 1\)-functions of semimartingales
cites work: Stochastic calculus with respect to continuous finite quadratic variation processes
cites work: Stochastic parabolic equations with anticipative initial condition
OpenAlex ID: W2964026371
title: Stochastic integration with respect to the cylindrical Wiener process via regularization
review text: The author defines an integral with respect to a cylindrical Brownian motion on a separable Hilbert space \(V\) with covariance matrix given by a self-adjoint operator \(V\) following the ideas of \textit{F. Russo} and \textit{P. Vallois} [Probab. Theory Relat. Fields 97, No. 3, 403--421 (1993; Zbl 0792.60046)] on integration via regularization. The defined integral is an extension of the classical one. The author's method is based on the representation of the stochastic integral with respect to the cylindrical Wiener process as a series of standard stochastic integrals with respect to components of the cylindrical Wiener process. As an application, he proves the existence of a solution of a parabolic stochastic partial differential equation with anticipating initial data.
reviewed by: Franco Fagnola
description: scientific article; zbMATH DE number 6222498