Probability theory and stochastic processes Stochastic processes: general theory Concept
Gaussian process
Summary
A Gaussian process is a stochastic process all of whose finite-dimensional distributions are multivariate normal. Its law is determined by its mean function and its covariance function, and any positive semidefinite covariance function arises. The Wiener process, the Brownian bridge, the Ornstein–Uhlenbeck process and fractional Brownian motion are Gaussian processes. In statistics and machine learning, Gaussian processes serve as prior distributions on unknown functions.
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| Tag | 22WEM6RTW0 |
|---|---|
| URI | m2://22WEM6RTW0 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 60G15 |
| Specializes | Stochastic process |
| Same as | |
| Changed | 2 November 2026 |
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Special cases
- Wiener process
- Brownian bridge
- Gaussian free field
- Ornstein–Uhlenbeck process
- Fractional Brownian motion