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.
September 2009
Monthly Archive
September 14, 2009