Path integral methods for stochastic equations

I’m currently in Edinburgh for a Mathematical Neuroscience workshop. I gave a tutorial today on using field theoretic methods to solve stochastic differential equations (SDE’s). The slides are here.  The methods I presented have been around for decades but as far as I know they haven’t been collated together into a pedagogical review for nonexperts.  Also, there is an entire community of theorists and mathematicians that are unaware of path integral methods.  In particular, I apply the response function formalism stemming from the work of Martin Siggia and Rose.  Field theory and diagrammatic methods are a nice way to organize perturbation expansions for nonlinear SDE’s.  I plan to write a review paper on this topic in the next few months and will post it here.

Addendum: Jan 20, 2011.  The review paper can be found here.


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