Definition:Mean of Stochastic Process

Definition

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

The mean of $S$ over an interval $Q$ is the arithmetic mean of the observations of $T$ over all the timestamps within $Q$.

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:

$2.1.2$ Stationary Stochastic Processes: Mean and variance of a stationary process