The Generalized Entropy Ergodic Theorem for Nonhomogeneous Markov Chains

Abstract

Let $({\xi }_n{)}_{n=0}^{\infty }$ be a nonhomogeneous Markov chain taking values from finite state-space of $\mathbf{X}=\{1,2,\dots ,b\}$. In this paper, we will study the generalized entropy ergodic theorem with almost-everywhere and ${\mathcal{L}}_1$ convergence for nonhomogeneous Markov chains, which generalizes the corresponding classical results for the Markov chains.

13 pages,This paper has been accepted for publication in Journal of Theoretical Probability