Diffusion process
For the marketing term, see Diffusion of innovations.
In probability theory and statistics, a diffusion process is a solution to a stochastic differential equation. It is a continuous-time Markov process with almost surely continuous sample paths. Brownian motion, reflected Brownian motion and Ornstein–Uhlenbeck processes are examples of diffusion processes.
A sample path of a diffusion process models the trajectory of a particle embedded in a flowing fluid and subjected to random displacements due to collisions with other particles, which is called Brownian motion. The position of the particle is then random; its probability density function as a function of space and time is governed by an advection–diffusion equation.
Mathematical definition
A diffusion process is a Markov process with continuous sample paths for which the Kolmogorov forward equation is the Fokker–Planck equation.[1]
See also
- Diffusion
- Itô diffusion
- Jump diffusion
- Sample-continuous process
References
- ^ "9. Diffusion processes" (pdf). Retrieved October 10, 2011.
This article is copied from an article on Wikipedia® - the free encyclopedia created and edited by its online user community. The text was not checked or edited by anyone on our staff. Although the vast majority of Wikipedia® encyclopedia articles provide accurate and timely information, please do not assume the accuracy of any particular article. This article is distributed under the terms of GNU Free Documentation License.