nLab stochastic process




A stochastic process is a function from a linearly ordered set TT (“time”, typically the integers or positive real axis) into a set of random variables (on fixed probability space), that is a collection (X t) tT(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.


With an eye towards quantum noise;

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