Journal of Mathematical Sciences

, Volume 75, Issue 1, pp 1461–1468 | Cite as

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

  • V. V. Chichagov
Probabilistic-Statistical Models


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.


Markov Chain Random Number Finite Number Discrete Time Limit Theorem 
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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. V. Chichagov
    • 1
  1. 1.Perm

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