Gaussian process

A stochastic processMathworldPlanetmath {X(t)tT} 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<, and any t1,,tnT, the joint distributionPlanetmathPlanetmath of random variablesMathworldPlanetmath X(t1),,X(tn) is jointly normal.

As an example, any Wiener processMathworldPlanetmath is Gaussian.

Remark. Sometimes, a Gaussian process is known as a Gaussian random field if T is a subset, usually an embedded manifold, of 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