Definition:Gaussian Process

Theorem

Let $S$ be a stochastic process giving rise to a time series $T$.

Let the probability distribution of $T$ be a multivariate normal distribution.

Then $S$ is called a Gaussian process.

Also known as

A Gaussian process is also known as a normal process.

Source of Name

This entry was named for Carl Friedrich Gauss.

Sources

• 1994: George E.P. Box, Gwilym M. Jenkins and Gregory C. Reinsel: Time Series Analysis: Forecasting and Control (3rd ed.) ... (previous) ... (next):

Part $\text {I}$: Stochastic Models and their Forecasting:

$2$: Autocorrelation Function and Spectrum of Stationary Processes:

$2.1$ Autocorrelation Properties of Stationary Models:

$2.1.3$ Positive Definiteness and the Autocovariance Matrix: Gaussian processes