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Asymptotic behavior of the first arrival time in Markovian random walks

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Abstract

The article examines the asymptotic behavior of the first arrival time for homogeneous Markov random walks with a fixed stopping boundary. Conditions of convergence to exponential and gamma distributions are established. The results are applied to solve one problem of statistical control.

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Literature cited

  1. C. -L. Chung, Homogeneous Markov Chains [Russian translation], Mir, Moscow (1964).

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  2. S. Kh. Sirazhdinov, Limit Theorems for Homogeneous Markov Chains [in Russian], Izd. Akad. Nauk Uzbek SSR, Tashkent (1955).

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  3. Ya. P. Lumel'skii and V. V. Chichagov, “Unbiased estimation of the case of homogeneous Markov chains,” in: Statisticheskie Metody, Perm (1980).

  4. R. Bellman, An Introduction to Matrix Theory [Russian translation], Nauka, Moscow (1976).

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  5. A. D. Solov'ev, “A combinatorial identity and its application to the problem of first occurrence of a rare event,” Teor. Veroyatn. Primen.,11, No. 2 (1966).

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Authors and Affiliations

  1. Perm University, USSR

    V. V. Chichagov

Authors
  1. V. V. Chichagov
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Additional information

Translated from Statisticheskie Metody, pp. 183–189, 1982.

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Chichagov, V.V. Asymptotic behavior of the first arrival time in Markovian random walks. J Math Sci 39, 2944–2948 (1987). https://doi.org/10.1007/BF01092349

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  • DOI: https://doi.org/10.1007/BF01092349

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