# Random Lie-point symmetries of stochastic differential equations

## TL;DR

This paper investigates the invariance properties of stochastic differential equations under random transformations, deriving conditions for symmetries in both Ito and Stratonovich frameworks.

## Contribution

It introduces the determining equations for random Lie-point symmetries of stochastic differential equations, extending symmetry analysis to stochastic contexts.

## Key findings

- Derived the determining equations for random Lie-point symmetries.
- Established relations between symmetries in Ito and Stratonovich forms.
- Connected results with previous literature on stochastic symmetries.

## Abstract

We study the invariance of stochastic differential equations under random diffeomorphisms, and establish the determining equations for random Lie-point symmetries of stochastic differential equations, both in Ito and in Stratonovich form. We also discuss relations with previous results in the literature.