On the uniform integrability of the Radon-Nikodym densities for Wiener measure
type: Item
instance of: scholarly article
title: On the uniform integrability of the Radon-Nikodym densities for Wiener measure
zbMATH Open document ID: 0952.60003
author: A. S. Üstünel
author: Moshe Zakai
published in: Journal of Functional Analysis
publication date: 2001-01-02T00:00:00Z
review text: The paper considers nonlinear transformations of the abstract Wiener space \((W,H,\mu)\). Especially, the invertibility of the mapping \(T:W\to{W}:w\mapsto{w+u(w)}\), where \(u:W\to{H}\) is ``small'', is in the center of the authors' interest. The paper presents a set of conditions under which the mapping \(T\) is invertible, the Radon-Nikodym density of \(T\) and of its inverse, both considered as random variables, can be evaluated. The results are applied for the description of a flow fulfilling a particular differential equation.
Mathematics Subject Classification ID: 60A10
Mathematics Subject Classification ID: 60H99
Mathematics Subject Classification ID: 60J60
zbMATH DE Number: 1268060
zbMATH Keywords: separable Banach space
zbMATH Keywords: separable Hilbert space
zbMATH Keywords: abstract Wiener space
zbMATH Keywords: Sobolev spaces of Wiener functionals
zbMATH Keywords: Radon-Nikodym derivative
zbMATH Keywords: flow of transformations
reviewed by: Petr Lachout
MaRDI profile type: Publication
full work available at URL: jfan.1998.3320
OpenAlex ID: W2038919318
cites work: Q3658220
cites work: Transformations of Wiener integrals under translations
cites work: The Transformation of Wiener Integrals by Nonlinear Transformations
cites work: Equations différentielles sur l'espace de Wiener et formules de Cameron- Martin non-linéaires
cites work: Q5581156
cites work: On the convergence of sums of independent Banach space valued random variables
cites work: Absolute Continuity and Radon-Nikodym Derivatives for Certain Measures Relative to Wiener Measure
cites work: Q3038308
cites work: Analysis on Wiener spaces. I: Nonlinear maps
cites work: Analysis on Wiener spaces. II: Differential forms
cites work: Q4337939
cites work: On nonlinear transformations of Gaussian measures
cites work: Q5601742
cites work: Q3857325
cites work: Transformation of Wiener measure under anticipative flows
cites work: Random rotations of the Wiener path
cites work: Some exponential moment inequalities for the Wiener functionals
cites work: Transformation of the Wiener measure under non-invertible shifts
cites work: Measures induced on Wiener space by monotone shifts
cites work: Q4765632
DOI: 10.1006/JFAN.1998.3320
description: scientific article; zbMATH DE number 1268060