Howtosignalprocessing
- How do you know if a process is ergodic?
- When can a random process is said to be an ergodic process co1 *?
- Does stationarity imply Ergodicity?
- When the time average of a random process is equal to its ensemble average the random process is?
How do you know if a process is ergodic?
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. In this regime, any collection of random samples from a process must represent the average statistical properties of the entire regime.
When can a random process is said to be an ergodic process co1 *?
A random process is said to be ergodic if the time averages of the process tend to the appropriate ensemble averages. This definition implies that with probability 1, any ensemble average of X(t) can be determined from a single sample function of X(t).
Does stationarity imply Ergodicity?
Yes, ergodicity implies stationarity. Consider an ensemble of realizations generated by a random process. Ergodicity states that the time-average is equal to the ensemble average. The time-average is obtained by taking the average of a single realization, giving you a particular number.
When the time average of a random process is equal to its ensemble average the random process is?
Since the time average equals the ensemble average, the process is ergodic in the mean. It is also true that Eq. (1.9) holds, so the process is ergodic in the correlation.
