# A symmetry-adapted numerical scheme for SDEs

## TL;DR

This paper introduces a geometric numerical scheme for stochastic differential equations that leverages Lie symmetries to preserve invariant properties, improving the accuracy and structure of numerical solutions.

## Contribution

The paper presents a symmetry-adapted numerical scheme for SDEs, utilizing Lie symmetries to maintain invariant properties during approximation.

## Key findings

- Applied to linear SDEs with successful symmetry preservation
- Established theoretical error estimates for the proposed scheme
- Demonstrated improved geometric properties in numerical solutions

## Abstract

We propose a geometric numerical analysis of SDEs admitting Lie symmetries which allows us to individuate a symmetry adapted coordinates system where the given SDE has notable invariant properties. An approximation scheme preserving the symmetry properties of the equation is introduced. Our algorithmic procedure is applied to the family of general linear SDEs for which two theoretical estimates of the numerical forward error are established.