# Symmetry of stochastic non-variational differential equations

## TL;DR

This paper explores how symmetry methods, traditionally used for deterministic differential equations, can be extended to analyze stochastic differential equations, highlighting recent developments and future perspectives.

## Contribution

It reviews classical symmetry theory for deterministic equations and discusses recent efforts to adapt these methods to stochastic differential equations.

## Key findings

- Symmetry methods aid in solving deterministic differential equations.
- Recent extensions of symmetry theory to stochastic equations are discussed.
- Perspectives for future research in stochastic symmetry analysis are outlined.

## Abstract

I will sketchily illustrate how the theory of symmetry helps in determining solutions of (deterministic) differential equations, both ODEs and PDEs, staying within the classical theory. I will then present a quick discussion of some more and less recent attempts to extend this theory to the study of stochastic differential equations, and briefly mention some perspective in this direction.