We discussed transformations of the Fokker-Planck equation. One of these eliminated an heterogeneous diffusion term. We discussed in detail an example of variable diffusion constant.
Today try a different approach.
Master equation approach considered time evolution of probability distribution. Fokker-Planck equation was derived from master equation typically from system size expansion . Let x stochastic variable. Clearly and we find We next generalize to take the limit and write the Langevin equation on the form where and with the Dirac -function. Noise with these properties called white .