Multiple Wiener integrals and nonlinear functionals of a nuclear space valued Wiener process
type: Item
instance of: scholarly article
title: Multiple Wiener integrals and nonlinear functionals of a nuclear space valued Wiener process
zbMATH Open document ID: 0627.60053
DOI: 10.1007/BF01442193
published in: Applied Mathematics and Optimization
publication date: 1987-01-01T00:00:00Z
review text: In this work we develop techniques for the study of nonlinear functionals of a \(\Phi'\)-valued Wiener process \(W_ t\), where \(\Phi'\) is the dual of a countably Hilbert nuclear space. We construct stochastic integrals and multiple Wiener integrals of operator-valued processes with respect to \(W_ t\). The Wiener decomposition of the space of \(\Phi'\)-valued nonlinear functionals of \(W_ t\) is established. We also obtain multiple stochastic integral expansions and representations of \(\Phi'\)-valued nonlinear functionals of \(W_ t\) as operator-valued stochastic integrals of Itô type.
Mathematics Subject Classification ID: 60H05
Mathematics Subject Classification ID: 60B05
zbMATH DE Number: 4020121
zbMATH Keywords: operator-valued processes
zbMATH Keywords: Wiener decomposition
zbMATH Keywords: multiple stochastic integral expansions
zbMATH Keywords: operator-valued stochastic integrals of Itô type
author: Víctor Pérez-Abreu
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01442193
OpenAlex ID: W1486652511
description: scientific article; zbMATH DE number 4020121