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 ,and any $t_1,\mathrm{\dots },t_n\in T$, the joint distribution of randomvariables $X(t_1),\mathrm{\dots },X(t_n)$ 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 ${ℝ}^m$, with $m>1$.