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An extension of Cramér's estimate for the absorption probability of a random walk

Published online by Cambridge University Press:  24 October 2008

E. Arjas
Affiliation:
Institute of Mathematics, Helsinki University of Technology, Otaniemi, Finland
T. P. Speed
Affiliation:
Department of Probability and Statistics, University of Sheffield, Sheffield, U.K.

Extract

Consider a real-valued random walk

which is defined on a Markov chain {Xn: n ≥ 0} with countable state space I. We assume that a matrix Q(.) = (qij(.)) is given such that

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

(1)Cinlar, E.Markov renewal theory. Adv. Appl. Prob. 1 (1969), 123187.CrossRefGoogle Scholar
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(8)Miller, H. D.A matrix factorization problem in the theory of random variables defined on a finite Markov chain. Proc. Cambridge Philos. Soc. 58 (1962), 268285.CrossRefGoogle Scholar
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(10)Presman, E.Factorization methods and boundary problems for sums of random variables given on Markov chains. Izv. Akad. Nauk USSR Ser. Mat. 33 (1969). (English translation. Amer. Math. Soc. (1971), 818852.)Google Scholar
(11)Vere-Jones, D.Ergodic properties of non-negative matrices, I. Pacific J. Math. 23 (1967), 601620.Google Scholar
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An extension of Cramér's estimate for the absorption probability of a random walk
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