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.