Applications of the degree theorem to absolute continuity on Wiener space
type: Item
instance of: scholarly article
title: Applications of the degree theorem to absolute continuity on Wiener space
zbMATH Open document ID: 0794.60033
DOI: 10.1007/BF01196731
publication date: 1994-08-15T00:00:00Z
review text: Let \((\Omega,H,P)\) be an abstract Wiener space and define a shift on \(\Omega\) by \(T(\omega)=\omega+F(\omega)\) where \(F\) is an \(H\)-valued random variable. We study the absolute continuity of the measures \(P \circ T^{-1}\) and \((\Lambda_ FP) \circ T^{-1}\) with respect to \(P\) by using the techniques of the degree theory of Wiener maps, where \[ \Lambda_ F=\text{det}_ 2 (1+\nabla F) \text{Exp} \{-\delta F- \textstyle{{1 \over 2}} | F |^ 2\}. \]
Mathematics Subject Classification ID: 60G30
Mathematics Subject Classification ID: 60H07
zbMATH DE Number: 569075
zbMATH Keywords: Girsanov theorem
zbMATH Keywords: abstract Wiener space
zbMATH Keywords: absolute continuity
zbMATH Keywords: Wiener maps
author: A. S. Üstünel
author: Moshe Zakai
MaRDI profile type: Publication
cites work: Q4735882
cites work: Degree theory for Wiener maps
cites work: Q4134602
cites work: Absolute Continuity and Radon-Nikodym Derivatives for Certain Measures Relative to Wiener Measure
cites work: Q4039796
cites work: Q3038308
cites work: Q3779535
cites work: Q3973616
cites work: Generalized stochastic integrals and the Malliavin calculus
cites work: On nonlinear transformations of Gaussian measures
cites work: Transformation of Wiener measure under anticipative flows
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569075