A Remark on Symmetry of Stochastic Dynamical Systems and Their Conserved Quantities

TL;DR

This paper explores the symmetry properties of stochastic differential systems of Stratonovich type and introduces methods to find new conserved quantities by applying symmetry operators, extending prior research.

Contribution

It extends previous work by Misawa on symmetries and conserved quantities in stochastic systems, providing new methods and detailed examples.

Findings

New conserved quantities derived from symmetry operators

Extended symmetry analysis for stochastic differential equations

Illustrative examples demonstrating the methods

Abstract

Symmetry properties of stochastic dynamical systems described by stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given by applying symmetry operators to known conserved quantities. Some detailed examples are presented.