# Gaussian process

A stochastic process $\{X(t)\mid t\in T\}$ is said to be a Gaussian process if all of the members of its f.f.d. (family of finite dimensional distributions) are joint normal distributions. In other words, for any positive integer $n<\infty$, and any $t_{1},\ldots,t_{n}\in T$, the joint distribution of random variables $X(t_{1}),\ldots,X(t_{n})$ is jointly normal.

As an example, any Wiener process is Gaussian.

Remark. Sometimes, a Gaussian process is known as a Gaussian random field if $T$ is a subset, usually an embedded manifold, of $\mathbb{R}^{m}$, with $m>1$.

Title Gaussian process GaussianProcess 2013-03-22 15:22:48 2013-03-22 15:22:48 CWoo (3771) CWoo (3771) 5 CWoo (3771) Definition msc 60G15 msc 60G60 Gaussian random field normal process