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Pseudo-Poisson approximation for Markov chains

Author

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  • Borovkov, K. A.
  • Pfeifer, D.

Abstract

We consider the problem of approximating the distribution of a Markov chain with 'rare' transitions in an arbitrary state space by that of the corresponding pseudo-Poisson process. Sharp estimates for both first- and second-order approximations are obtained. The remarkable fact is that the convergence rate in this setup can be better than that in the ordinary Poisson theorem: the ergodicity of the embedded 'routing' Markov chain improves essentially the degree of approximation. This is of particular importance if the accumulated transition intensity of the chain is of a moderate size so that neither the usual estimates from the Poisson theorem nor the existence of a stationary distribution alone provide good approximation results. On the other hand, the estimates also improve the known results in the ordinary Poisson theorem.

Suggested Citation

  • Borovkov, K. A. & Pfeifer, D., 1996. "Pseudo-Poisson approximation for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 61(1), pages 163-180, January.
    • Handle: RePEc:eee:spapps:v:61:y:1996:i:1:p:163-180
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    References listed on IDEAS

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    1. Witte, Hans-Jürgen, 1993. "On the optimality of multivariate Poisson approximation," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 75-88, January.
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    Cited by:

    1. Cekanavicius, V. & Mikalauskas, M., 1999. "Signed Poisson approximations for Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 205-227, August.

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