Transformations of Wiener measure and orthogonal expansions

Abstract

In this paper we study the structure of square integrable functionals measurable with respect to coalescing stochastic flows. The case of the Wiener process stopped at the moment of hitting an irregular continuous level is considered. Relying on the change of measure technique, we present a new construction of multiple stochastic integrals with respect to stopped Wiener process. An intrinsic analogue of the Itô–Wiener expansion for the space of square integrable functionals measurable with respect to the stopped Wiener process is constructed.