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

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    • 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
    • Dates

  • Proceedings – Mathematical Sciences | News

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