• Markov approximation and the generalized entropy ergodic theorem for non-null stationary process

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/130/0013

• # Keywords

$m$-th order nonhomogeneous Markov chains; non-null stationary process; canonical approximation

• # Abstract

In an earlier work, we proved a generalized entropy ergodic theorem forfinite nonhomogeneous Markov chains (NMC). In this paper, we establish a generalized strong law of large numbers for finite $m$-th order NMC. Then we deduce a generalized entropy ergodic theorem for finite $m$-th order NMC, under some assumptions on the continuity rate and of non-nullness. Explicit upper and lower bounds relating the generalized relative entropy density of the original finite non-null stationary sequence and its canonical $m$-order Markov approximation is obtained.

• # Author Affiliations

1. School of Mathematics and Physics Science and Engineering, Anhui University of Technology, Ma’anshan 243002, China
2. Faculty of Science, Jiangsu University, Zhenjiang 212013, China

• # Proceedings – Mathematical Sciences

Volume 131, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019