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Poisson equation, moment inequalities and quick convergence for Markov random walks

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  • Fuh, Cheng-Der
  • Zhang, Cun-Hui

Abstract

We provide moment inequalities and sufficient conditions for the quick convergence for Markov random walks, without the assumption of uniform ergodicity for the underlying Markov chain. Our approach is based on martingales associated with the Poisson equation and Wald equations for the second moment with a variance formula. These results are applied to nonlinear renewal theory for Markov random walks. A random coefficient autoregression model is investigated as an example.

Suggested Citation

  • Fuh, Cheng-Der & Zhang, Cun-Hui, 2000. "Poisson equation, moment inequalities and quick convergence for Markov random walks," Stochastic Processes and their Applications, Elsevier, vol. 87(1), pages 53-67, May.
    • Handle: RePEc:eee:spapps:v:87:y:2000:i:1:p:53-67
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    References listed on IDEAS

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    1. Irle, A., 1993. "r-quick convergence for regenerative processes with applications to sequential analysis," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 319-329, April.
    2. Alsmeyer, Gerold, 1990. "Convergence rates in the law of large numbers for martingales," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 181-194, December.
    3. Alsmeyer, Gerold, 1994. "On the Markov renewal theorem," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 37-56, March.
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    Cited by:

    1. Fuh, Cheng-Der, 2021. "Asymptotic behavior for Markovian iterated function systems," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 186-211.

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