On the uniform integrability of the Radon-Nikodym densities for Wiener measure
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.
scientific article; zbMATH DE number 1268060
scientific article