Gaussian process

高斯过程

Probability · Graduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A real stochastic process for which every finite vector of observations has a multivariate normal distribution, allowing degenerate Gaussian vectors.

任意有限个时刻的观测组成的向量均服从多元正态分布的实值过程，允许退化情形。

Example

The constant-in-time process Xt=ZX_t=Z with Z∼N(0,1)Z\sim N(0,1) is Gaussian but not Brownian.

Usage and distinctions

Gaussian one-dimensional marginals do not by themselves guarantee that every observation vector is jointly Gaussian.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Rick Durrett — Probability: Theory and Examples, fifth edition§7.1 Brownian Motion, equivalent Gaussian-process formulation (a0)–(c0) · Checked 2026-10-14

Translation sources

  1. 李东风 — 应用随机过程，第7章 布朗运动（北京大学）§7.1.3 高斯过程，定义7.2 · Checked 2026-10-14
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