2013, pp 2000-2004

# Stochastic Processes, Fokker-Planck Equation

This is an excerpt from the content

### Synonyms

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

### Definition

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 ...
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9468948245048523, "perplexity": 303.74239769049296}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1413507444774.49/warc/CC-MAIN-20141017005724-00069-ip-10-16-133-185.ec2.internal.warc.gz"}