Transformations of Wiener measure and orthogonal expansions

The main objective of the talk will be to discuss analogues of the Itô-Wiener expansion for measures defined as transformations of the Wiener measure by coalescing type mappings. The totality of a family of specific multiple stochastic intergals in $L^2$ relatively to the transformed measure will be proved. In certain cases an explicit formula for calculating the orthogonal expansion will be proposed. This formula is a generalization of the Krylov-Veretennikov formula. Obtained results will be applied to the study of an orthogonal structure of the space of square integrable functions measurable with respect to the Arratia flow.