# Ergodic process and random walk

Is a gaussian random walk process an ergodic process? If Yes, does someone knows the proof?

Thanks in advance

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Well, it has independent increments, so... –  Chris Taylor Feb 22 '12 at 19:01

## 1 Answer

No. The standard random walk has no invariant distribution. The solution is N(0,t) for $t<\infty$. The OU process (with drift towards 0) is ergodic.

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