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Strong ergodicity of monotone transition functions

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  • Zhang, Hanjun
  • Chen, Anyue
  • Lin, Xiang
  • Hou, Zhenting
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    Abstract

    By revealing close links among strong ergodicity, monotone, and the Feller-Reuter-Riley (FRR) transition functions, we prove that a monotone ergodic transition function is strongly ergodic if and only if it is not FRR. An easy to check criterion for a Feller minimal monotone chain to be strongly ergodic is then obtained. We further prove that a non-minimal ergodic monotone chain is always strongly ergodic. The applications of our results are illustrated using birth-and-death processes and branching processes.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 55 (2001)
    Issue (Month): 1 (November)
    Pages: 63-69

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    Handle: RePEc:eee:stapro:v:55:y:2001:i:1:p:63-69

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    Related research

    Keywords: Feller minimal transition functions Monotone transition functions Feller-Reuter-Riley transition functions Feller-Reuter-Riley q-matrices Ordinary ergodicity Strong ergodicity Zero-entrance;

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    Cited by:
    1. Li, Yangrong, 2007. "Strongly monotone q-functions and a note on strong ergodicity of monotone q-functions," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 396-400, February.

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