Diffusion process: Difference between revisions

Revision as of 04:39, 16 February 2023

Revision as of 15:30, 16 February 2023

Line 1:

{{Short description|Solution to a stochastic differential equation}}

{{for|the marketing term|Diffusion of innovations}}

In [[probability theory]] and [[statistics]], '''diffusion processes''' are a class of continuous-time stochastic [[Markov process]] with [[almost surely]] [[continuous function|continuous]] sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic systems. [[Brownian motion]], [[reflected Brownian motion]] and [[Ornstein–Uhlenbeck processes]] are examples of diffusion processes. It is used heavily in [[statistical physics]], [[statistical analysis]], [[information theory]], [[data science]], [[neural networks]], [[finance]] and [[marketing]].

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 equation|advection]]–[[diffusion equation]].