In physics, statistics, econometrics and signal processing, a stochastic process is said to be in an ergodic regime if an observable's ensemble average equals the time average.
[1] In this regime, any collection of random samples from a process must represent the average statistical properties of the entire regime.
[2] A regime implies a time-window of a process whereby ergodicity measure is applied.
One can discuss the ergodicity of various statistics of a stochastic process.
For example, a wide-sense stationary process
has constant mean and autocovariance that depends only on the lag
are ensemble averages (calculated over all possible sample functions
is said to be mean-ergodic[3] or mean-square ergodic in the first moment[4] if the time average estimate converges in squared mean to the ensemble average
Likewise, the process is said to be autocovariance-ergodic or d moment[4] if the time average estimate converges in squared mean to the ensemble average
A process which is ergodic in the mean and autocovariance is sometimes called ergodic in the wide sense.
The notion of ergodicity also applies to discrete-time random processes
Each operator in a call centre spends time alternately speaking and listening on the telephone, as well as taking breaks between calls.
Each break and each call are of different length, as are the durations of each 'burst' of speaking and listening, and indeed so is the rapidity of speech at any given moment, which could each be modelled as a random process.
Each resistor has an associated thermal noise that depends on the temperature.
Now take a particular instant of time in all those plots and find the average value of the voltage.