A **stochastic process** is a function from a linearly ordered set $T$ (“time”, typically the integers or positive real axis) into a set of random variables (on fixed probability space), that is a collection $(X_t)_{t\in T}$ of random variables.

By a **random process** physicists usually mean the same, but mathematicians sometimes allow random processes indexed by more general sets, not usually with meaning of time or equipped with a linear order; maybe “random collection” would be a better term in that case.

The most studied examples include Brownian motion, Ornstein-Uhlenbeck process? and Lévy process?es.

- Wikipedia stochastic process

With an eye towards quantum noise;

- Stéphane Attal,
*Stochastic Processes*, Lecture 4 in:*Lectures on Quantum Noises*[pdf, webpage]

Last revised on November 25, 2022 at 10:23:16. See the history of this page for a list of all contributions to it.