# Is ergodicity defined for a stochastic process not necessarily wide-sense stationary?

From ergodic process in Wikipedia, the definition of an ergodic process seems informal, and doesn't seem to require the stochastic process to be wide-sense stationary.

But in order to make the ergodic moments (mean and covariance) to be the same as the ensemble ones, it makes sense when the ensembel means and covariances do not change with time.

So I wonder if ergodicity can be defined for a stochastic process not necessarily wide-sense stationary?

Thanks and regards!

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You might want to look on dsp.SE at the discussions following this question and this other one for an engineering perspective on the matter. –  Dilip Sarwate Dec 2 '12 at 22:49
Thanks, @DilipSarwate! I did see your reply in the first link when I did some google search before asking. My question is: if $E(X_t)$ changes with $t$, how is ergodicity defined for the stochastic process $(X_t)$? For example, how about redefining it to be the ergodic mean equal $\lim_{t \to \infty} E(X_t)$, which however requires $\lim_{t \to \infty} E(X_t)$ to exist? –  Tim Dec 2 '12 at 22:52