Embedding the abstract Wiener space in a probability space
type: Item
instance of: scholarly article
title: Embedding the abstract Wiener space in a probability space
zbMATH Open document ID: 0947.60068
published in: Journal of Functional Analysis
publication date: 2000-08-28T00:00:00Z
review text: Consider an abstract Wiener process \((W,w,H)\), embedded in a probability space \((\Omega,{\mathcal F},\mathbb{P})\), in the sense that \(w\) is a \(W\)-valued Gaussian variable, with \(H\) as reproducing space. On the one hand, a simple conditional Malliavin calculus is defined, by differentiating only in the direction of \(w\). On the other hand, an Itô integral is constructed, starting from an adapted continuous resolution of identity on \(H\). These two extensions are applied to a filtering problem, yielding dimension-free Girsanov-like formulas, and to a representation of martingale results.
reviewed by: Jacques Franchi
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60H30
zbMATH DE Number: 1423455
zbMATH Keywords: Wiener space
zbMATH Keywords: Malliavin calculus
zbMATH Keywords: Itô integral
zbMATH Keywords: Girsanov formula
zbMATH Keywords: filtering problem
author: A. S. Üstünel
author: Moshe Zakai
MaRDI profile type: Publication
full work available at URL: jfan.1999.3485
OpenAlex ID: W2015261491
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DOI: 10.1006/JFAN.1999.3485
description: scientific article; zbMATH DE number 1423455