Transformations of Wiener Measure and Orthogonal Expansions

2013/10/17 by Andrey A. Dorogovtsev, Dorogovtsev, Andrey A., Georgii V. Riabov +1
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1310.4722

arxiv created 2013/10/23 · arxiv updated 2013/10/24

Abstract

In this paper we study the structure of square integrable functionals measurable with respect to coalescing stochastic flows. The case of L² space generated by the process η(⋅)=w(min(τ,⋅)), where w is a Brownian motion and τ is the first moment when w hits the given continuous function g is considered. We present a new construction of multiple stochastic integrals with respect to the process η. Our approach is based on the change of measure technique. The analogue of the Itô-Wiener expansion for the space L²(η) is constructed.

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