Suppose $$dX_t = \mu(X_t,t)dt + \sigma(X_t,t)dW_t$$ is a 1D nonlinear stochastic differential equation ($dW_t$ is typically assumed to be Brownian). According to wikipedia the distribution of $X_t$ at any instant obeys $$ \frac{\partial p(x,t)}{\partial t} = -\frac{\partial}{\partial x}(\mu(x,t) p(x,t)) + \frac{\partial^2}{\partial x^2}(D(x,t)p(x,t)). $$

which is known as the Fokker-Planck equation (in 1D). I'm interested in developing this into a path integral. Some sketches are given at the bottom of the wiki page, but it's very difficult to understand them. Is there a standard reference here? There is one on the page, but it is rather specific to critical phenomena.


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