Gaussian process

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

单词	GaussianProcess
释义	Gaussian process A stochastic process $\\{X(t)\\mid t\\in T\\}$ is said to bea Gaussian process if all of the members of its f.f.d.(family of finite dimensional distributions) are joint normaldistributions. In other words, for any positive integer $n<\\infty$ ,and any $t_{1},\\ldots,t_{n}\\in T$ , the joint distribution of randomvariables $X(t_{1}),\\ldots,X(t_{n})$ 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 $m>1$ .
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