Abstract
The Fokker Planck equation (FPE) , a special type of master equation, is a partial differential equation for time evolution of the PDF that describes Markov processes. A FPE is obtained from a Markov process when the two lowest moments of the jump characteristic of the drift and the fluctuation are given. The diffusion equation and the Smoluchowski equation for Brownian motion we studied fall into this category.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Further Reading and References
N.G. Van Kampen, Stochastic Processes in Physics and Chemistry, 2nd edn. (Elsevier, North Holland, 2003)
C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd edn. (Springer, 1985)
H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications, 2nd edn. (Springer, Berlin, Heidelberg, New York, 1989)
W. Ebeling, I.M. Sokolov, Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems (World Scientific Publishing Co. Pte. Ltd., 1992)
D.T. Gillespie, Markov Processes: An Introduction for Physical Scientists (Academic Press, San Diego, 1992)
R. Kubo, M. Toda, N. Hashitsume, Statistical Physics II, Nonequilibrium Statistical Mechanics, 2nd edn. (Springer, Berlin, Heidelberg, 1991)
R. Zwanzig, Nonequilibrium Statistical Machanics (Oxford University Press, Oxford, 2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature B.V.
About this chapter
Cite this chapter
Sung, W. (2018). Theory of Markov Processes and the Fokker-Planck Equations. In: Statistical Physics for Biological Matter. Graduate Texts in Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1584-1_15
Download citation
DOI: https://doi.org/10.1007/978-94-024-1584-1_15
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-024-1583-4
Online ISBN: 978-94-024-1584-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)