Some properties of Rényi entropy and Rényi entropy rate

In this paper, we define the conditional Rényi entropy and show that the so-called chain rule holds for the Rényi entropy. Then, we introduce a relation for the rate of Rényi entropy and use it to derive the rate of the Rényi entropy for an irreducible-aperiodic Markov chain. We also show that the bound for the Rényi entropy rate is simply the Shannon entropy rate.