# Definition:Gaussian Process

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## 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

- $2.1$ Autocorrelation Properties of Stationary Models:

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

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