# 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 $$,
and any ${t}_{1},\mathrm{\dots},{t}_{n}\in T$, the joint distribution^{} of random
variables^{} $X({t}_{1}),\mathrm{\dots},X({t}_{n})$ 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 ${\mathbb{R}}^{m}$, 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 |