Consider a discrete Markov source, ona finite alphabet set. Let the initial distribution be and the transition probability for the step be . When can we say that is stationary?

Clearly, the source has to be time invariant and thefore we need . For to be stationary, we need

etc, where is the distribution. But . Thus guarantees that all ‘s have the same distribution. Now, consider, say, and .

It is clear that for the two joint distributions to be equal, is enough and therefore is sufficient.

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