Reference Work Entry

Encyclopedia of Systems Biology

pp 2000-2004

Stochastic Processes, Fokker-Planck Equation

  • Hong QianAffiliated withDepartment of Applied Mathematics, University of Washington Email author 
  • , Hao GeAffiliated withSchool of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University


Diffusion approximation to chemical master equation; Diffusion processes; Kolmogorov forward equation; Smoluchowski equation; Stochastic differential equation


The Fokker–Planck equation describes the time evolution of the probability density function of the position of a particle that follows a stochastic differential equation. It is assumed that the sample trajectories of the particle are continuous functions of time; but they are nowhere differentiable with respect to time. It is a generalization of the diffusion equation with the presence of a drift force field. It is named after A. Fokker and M. Planck; It is also known as the Kolmogorov forward equation, named after A. Kolmogorov. The first use of the Fokker–Planck equation was for the statistical description of Brownian motion of a particle in a fluid, independently, by A. Einstein and M. von Smoluchowski. Diffusion motion can be considered as a limiting case of biased random walk.

In one spatial ...

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