Portrait of Raghav Somani

Raghav Somani

Quantitative Researcher

Deriving the Fokker-Planck equation

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In the theory of dynamical systems, the Fokker–Planck equation describes the time evolution of a probability density function. It describes how the density of a stochastic process changes over time under the influence of a potential field. Common applications include Brownian motion, the Ornstein–Uhlenbeck process, and statistical physics. Here I record a formal derivation of the partial differential equation by deriving a master equation and using a Taylor series to obtain the Kramers–Moyal expansion. A special case of the finite expansion is called the Fokker–Planck equation.

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