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# 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 $m>1$.

Defines:

normal process

Synonym:

Gaussian random field

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

60G15*no label found*60G60

*no label found*

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