Entropy Rates For Markov Chains
Since a stochastic process defined by a Markov chain that is irreducible and aperiodic has a stationary distribution, the entropy rate is independent of the initial distribution.
For example, for such a Markov chain Yk defined on a countable number of states, given the transition matrix Pij, H(Y) is given by:
where μi is the stationary distribution of the chain.
A simple consequence of this definition is that the entropy rate of an i.i.d. stochastic process has an entropy rate that is the same as the entropy of any individual member of the process.
Read more about this topic: Entropy Rate
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