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Limit theorems for Markov random walks with a fixed number of certain transitions

  • Probabilistic-Statistical Models
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Abstract

The limit behavior of Markov chains with discrete time and a finite number of states (MCDT) depending on the number n of its steps has been almost completely investigated [1–4]. In [5], MCDT with forbidden transitions were investigated, and in [6], the sum of a random number of functionals of random variables related by a homogeneous Markov chain (HMC) was considered. In the present paper, we continue the investigation of the limit behavior of the MCDT with random stopping time which is determined by a Markov walk plan II with a fixed number of certain transitions [7, 8]. Here we apply a method similar to that of [6], which allows us to obtain, together with some generalizations of the results of [6], a number of new assertions.

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Authors and Affiliations

  1. Perm

    V. V. Chichagov

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  1. V. V. Chichagov
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Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 119–130, Perm, 1990.

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Chichagov, V.V. Limit theorems for Markov random walks with a fixed number of certain transitions. J Math Sci 75, 1461–1468 (1995). https://doi.org/10.1007/BF02362560

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  • DOI: https://doi.org/10.1007/BF02362560

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