A note on supersymmetry and stochastic differential equations

TL;DR

This paper explores the connection between supersymmetry and stochastic differential equations, demonstrating a dimensional reduction in their law through a supersymmetric representation.

Contribution

It introduces a supersymmetric approach to analyze stochastic differential equations, extending the Parisi-Sourlas representation to obtain dimensional reduction results.

Findings

Dimensional reduction for certain stochastic differential equations.

Application of supersymmetry to stochastic analysis.

Extension of Parisi-Sourlas representation.

Abstract

We obtain a dimensional reduction result for the law of a class of stochastic differential equations using a supersymmetric representation first introduced by Parisi and Sourlas.