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.
December 8, 2011 at 12:15
[...] http://sciencehouse.wordpress.com/2009/03/22/path-integral-methods-for-stochastic-equations/ [...]
October 10, 2012 at 10:23
[...] equations perturbatively. The slides are the same as the tutorial I gave a few years ago (see here). I slightly modified the review paper that goes with the talk. I added the explicit computation [...]