Ornstein-Uhlenbeck process

The Ornstein-Uhlenbeck process is a type of stochastic process that models phenomena evolving over time. It is a Markov process with stationary transition probabilities, meaning its future behavior depends only on its current state, not its entire past history.1

This process is a more sophisticated model for Brownian motion than Einstein's original formulation. It describes the velocity of a particle subject to friction and random molecular collisions. Unlike basic Brownian motion, the Ornstein-Uhlenbeck process has a well-defined velocity at each point in time. It is also used in queuing models and as an approximation for other complex stochastic processes.23