A brief, opinionated introduction to the Fokker-Planck equation

Notes for the INM-6 book club of 12 August 2022, given by Alexandre René and Alexander van Meegen.

The presentation is split into three parts:

• Derivation of the Fokker-Planck equation (FPE) from the Kramers-Moyal expansion

• Tight relationship between stochastic differential equations and the FPE.

• Picturing probability flow as advection-diffusion in a fluid.

The first parts are based on the classic text by Risken [1996].