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In stochastic processes, Kramers–Moyal expansion refers to a Taylor series expansion of the master equation, named after Hans Kramers and José Enrique Moyal. This expansion transforms the integro-differential master equation
where p {\displaystyle p} {\displaystyle p} ] is the transition probability density, to an infinite order partial differential equation
where
Here W {\displaystyle W} is the transition probability rate. The Fokker–Planck equation is obtained by keeping only the first two terms of the series in which α 1 {\displaystyle \alpha _{1}} is the drift and α 2 {\displaystyle \alpha _{2}} is the diffusion coefficient.