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arXiv · 1310.4722

Transformations of Wiener Measure and Orthogonal Expansions

Andrey A. Dorogovtsev·Georgii V. Riabov
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Abstract

In this paper we study the structure of square integrable functionals measurable with respect to coalescing stochastic flows. The case of $L^2$ space generated by the process $η(\cdot)=w(\min(τ,\cdot)),$ 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 $L^2(η)$ is constructed.

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Andrey A. Dorogovtsev, Georgii V. Riabov. 2013-10-23. Transformations of Wiener Measure and Orthogonal Expansions. https://arxiv.org/abs/1310.4722

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