Proof of the polar decomposition of the Wiener measure

TL;DR

This paper provides a proof of the polar decomposition of the Wiener measure based on the orbits of the diffeomorphism group, advancing the mathematical understanding of Wiener measure structure.

Contribution

It offers a rigorous proof of the polar decomposition of Wiener measure with respect to diffeomorphism group orbits, a novel mathematical result.

Findings

Established the polar decomposition of Wiener measure

Connected Wiener measure with diffeomorphism group orbits

Enhanced understanding of measure transformations in stochastic analysis

Abstract

In the paper, we give the proof of the polar decomposition of the Wiener measure according to the orbits of the group of diffeomorphisms.