Stochastic path integrals can be derived like quantum mechanical path integrals
Abstract
Stochastic mechanics---the study of classical stochastic systems governed by things like master equations and Fokker-Planck equations---exhibits striking mathematical parallels to quantum mechanics. In this article, we make those parallels more transparent by presenting a quantum mechanics-like formalism for deriving a path integral description of systems described by stochastic differential equations. Our formalism expediently recovers the usual path integrals (the Martin-Siggia-Rose-Janssen-De Dominicis and Onsager-Machlup forms) and is flexible enough to account for different variable domains (e.g. real line versus compact interval), stochastic interpretations, arbitrary numbers of variables, explicit time-dependence, dimensionful control parameters, and more. We discuss the implications of our formalism for stochastic biology.
Cite
@article{arxiv.1909.12990,
title = {Stochastic path integrals can be derived like quantum mechanical path integrals},
author = {John J. Vastola and William R. Holmes},
journal= {arXiv preprint arXiv:1909.12990},
year = {2019}
}
Comments
39 pages, 2 tables. Will be submitted to Physical Review E