# Generalized Fokker-Planck equation

Consider the diffusion process $$d X = \mu(X, t) dt + \sigma(X, t) dY.$$ When $$Y$$ is a Brownian motion, we know that the density follows the Fokker-Planck equation. Here I'm considering the general case where $$Y$$ is an independent and stationary process such as the Poisson process or a weighted sum of a Brownian motion and a Poisson process. How can we derive the associated Fokker-Planck equation? Thanks!