Stochastic Euler-Poincar\'e reduction

TL;DR

This paper establishes a stochastic version of the Euler-Poincaré reduction theorem for processes on Lie groups, with applications demonstrated on SO(3) and diffeomorphism groups.

Contribution

It introduces a novel stochastic Euler-Poincaré reduction theorem applicable to Lie group-valued processes, expanding classical deterministic reduction methods.

Findings

Proves a stochastic Euler-Poincaré reduction theorem.

Provides applications to SO(3) and diffeomorphism groups.

Extends classical reduction techniques to stochastic processes.

Abstract

We prove a Euler-Poincar\'e reduction theorem for stochastic processes taking values in a Lie group and we show examples of its application to SO(3) and to the group of diffeomorphisms.