Electronic Resource
Springer
Probability theory and related fields
4 (1966), S. 354-373
ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We study the question of geometric ergodicity in a class of Markov chains on the state space of non-negative integers for which, apart from a finite number of boundary rows and columns, the elements pjk of the one-step transition matrix are of the form c k-j where {c k} is a probability distribution on the set of integers. Such a process may be described as a general random walk on the non-negative integers with boundary conditions affecting transition probabilities into and out of a finite set of boundary states. The imbedded Markov chains of several non-Markovian queueing processes are special cases of this form. It is shown that there is an intimate connection between geometric ergodicity and geometric bounds on one of the tails of the distribution {c k}.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00539120
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