Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

TL;DR

This paper explores how symmetry methods, including invariants and asymptotic techniques, can be extended from deterministic to stochastic differential equations, with explicit examples demonstrating the approach.

Contribution

It introduces an extension of symmetry methods to stochastic differential equations, combining invariants and asymptotic analysis.

Findings

Extended symmetry concepts to stochastic equations

Provided explicit examples illustrating the methods

Demonstrated the applicability of asymptotic symmetry analysis

Abstract

We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the deterministic one, such as conditional, partial and asymptotic symmetries. A number of explicit examples are presented.