# Basic Concepts of Random Processes

Definitions :: Ergodicity :: Autocorrelations :: Sinusoidal :: Poisson :: Gaussian :: Properties :: Spectra :: Cases :: Random :: Independent

## Ergodicity

Assume throughout that is stationary.

Loosely speaking, a random process
is
*
ergodic
*
if time
averages are equal to ensemble averages. That is, averages over
-- expectations -- are the same as averages over
. That
is, ensemble averages are the same as sample averages.

Here is an example: Suppose
is an i.i.d. sequence. The
ensemble mean is
. The sample mean is

By the S.L.L.N. we have

This is an example of an ergodic property.