Diffusion process - Wikipedia

In probability theory and statistics, diffusion processes are a class of continuous-time stochastic Markov process with almost surely continuous sample paths. 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–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]

References

^ "9. Diffusion processes" (pdf). Retrieved October 10, 2011.

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Mathematical definition

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References