Functional Methods in Stochastic Systems

TL;DR

This paper reviews the field-theoretic approach to representing solutions of stochastic differential equations and master equations, introducing a generic generating function and discussing ambiguities and variational methods.

Contribution

It presents a unified functional framework for stochastic systems, including a generic generating function and analysis of ambiguities in the representations.

Findings

A generic expression for the generating function of Green functions is proposed.

Relations between ambiguities in stochastic equations and functional representations are discussed.

Ordinary differential equations for expectations and correlations are derived using a variational approach.

Abstract

Field-theoretic construction of functional representations of solutions of stochastic differential equations and master equations is reviewed. A generic expression for the generating function of Green functions of stochastic systems is put forward. Relation of ambiguities in stochastic differential equations and in the functional representations is discussed. Ordinary differential equations for expectation values and correlation functions are inferred with the aid of a variational approach.