# Definition:Statistical Equilibrium

## Definition

Let $S$ be a stochastic process.

Suppose that the observations of the time series to which $S$ gives rise have a constant mean level.

Then $S$ is said to be in (statistical) equilibrium.

## Sources

$1$: Introduction:
$1.2$ Stochastic and Deterministic Dynamic Mathematical Models:
$1.2.1$ Stationary and Nonstationary Stochastic Models for Forecasting and Control
Part $\text {I}$: Stochastic Models and their Forecasting:
$2$: Autocorrelation Function and Spectrum of Stationary Processes
Part $\text {I}$: Stochastic Models and their Forecasting:
$2$: Autocorrelation Function and Spectrum of Stationary Processes:
$2.1$ Autocorrelation Properties of Stationary Models:
$2.1.2$ Stationary Stochastic Processes