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

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      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

       

      ZHONGZHI WANG1 WEIGUO YANG2

      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
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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