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Üstünel, Ali Süleyman; Zakai, Moshe

On the uniform integrability of the Radon-Nikodym densities for Wiener measure. (English) Zbl 0952.60003

J. Funct. Anal. 159, No. 2, 642-663 (1998).
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.
Reviewer: P.Lachout (Praha)

Cited in 1 Document

MSC:

60A10 Probabilistic measure theory
60H99 Stochastic analysis
60J60 Diffusion processes

Keywords:

separable Banach space; separable Hilbert space; abstract Wiener space; Sobolev spaces of Wiener functionals; Radon-Nikodym derivative; flow of transformations
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