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
Canonical name	GaussianProcess
Date of creation	2013-03-22 15:22:48
Last modified on	2013-03-22 15:22:48
Owner	CWoo (3771)
Last modified by	CWoo (3771)
Numerical id	5
Author	CWoo (3771)
Entry type	Definition
Classification	msc 60G15
Classification	msc 60G60
Synonym	Gaussian random field
Defines	normal process