Path Integral Methods for Stochastic Differential Equations

Path Integral Methods for Stochastic Differential Equations
A pedagogical paper (Path Integral Methods for Stochastic Differential) on how to use path integral and diagrammatic methods to solve stochastic differential equations perturbatively. The paper was originally written as a companion to a lecture by Carson Chow on the same topic at the 2009 mathematical neuroscience workshop in Edinburgh. The slides are available on the website.

The material could be suitable for a section in a “methods in applied math” or an “applied dynamical systems” course for first year graduate students or advanced undergraduates. It forgoes any semblance of rigor in favor of demonstrating practical ways to compute quantities such as moments and cumulants for nonlinear SDEs. We have also used these same methods to compute fluctuations and correlations around mean field theory in deterministic high dimensional dynamical systems although we do not explicitly cover this topic in this paper. The methods we introduce are well established in statistical mechanics and quantum field theory but are not well known in dynamical systems. We hope that this paper takes the mystery out of path integrals and Feynman diagrams and show that they are merely a convenient means to organize a perturbation expansion that can be applied to a variety of problems.
Author Institutional Affiliation
Carson Chow and Michael Buice
Tutorial LevelAdvanced Tutorial
Contest EntryYes

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