Supersymmetric formulation of multiplicative white--noise stochastic processes

TL;DR

This paper introduces a supersymmetric framework for Markov processes with multiplicative white-noise, capturing equilibrium properties and unifying different stochastic integral prescriptions without dependence on specific Wiener integral definitions.

Contribution

It provides a novel supersymmetric formulation that encodes equilibrium properties and treats various stochastic prescriptions uniformly.

Findings

Encodes fluctuation-dissipation relations through hidden symmetry.

Unifies different Wiener integral prescriptions in a single formalism.

Applicable to various equilibrium distributions at long times.

Abstract

We present a supersymmetric formulation of Markov processes, represented by a family of Langevin equations with multiplicative white-noise. The hidden symmetry encodes equilibrium properties such as fluctuation-dissipation relations. The formulation does not depend on the particular prescription to define the Wiener integral. In this way, different equilibrium distributions, reached at long times for each prescription, can be formally treated on the same footing.