In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths.
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 a convection–diffusion equation.
A diffusion process is a Markov process with continuous sample paths for which the Kolmogorov forward equation is the Fokker–Planck equation.