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Levels of null persistency for Markov chains

Published online by Cambridge University Press:  14 July 2016

Dean Isaacson  and
Peter Colwell
Dean Isaacson*
Affiliation:
Iowa State University
Peter Colwell*
Affiliation:
Iowa State University
*
∗ Postal address: Department of Mathematics, Carver Hall, Iowa State University, Ames, IA50011, U.S.A.
∗ Postal address: Department of Mathematics, Carver Hall, Iowa State University, Ames, IA50011, U.S.A.
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Abstract

In the study of null-persistent Markov chains the sequence plays an important role. (See for example, Orey (1971), Athreya and Ney (1980).) In this paper we consider the rate of growth of UN to ∞ as N → ∞. This rate of growth is related to the rate of growth of as N → ∞ and also to the rate at which as n → ∞.

Keywords

IRREDUCIBLENULL PERSISTENTHOMOGENEOUSMARKOV CHAIN
Type
Short Communications
Information
Journal of Applied Probability , Volume 19 , Issue 2 , June 1982 , pp. 425 - 429
Copyright
Copyright © Applied Probability Trust 1982 

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References

Athreya, K. B. and Ney, P. (1980) A new approach to the limit theory of recurrent Markov chains. Trans. Amer. Math. Soc. 245, 493–501.Google Scholar
Doeblin, W. (1938) Sur deux problèmes de M. Kolmogoroff concernant les chains dénombrales. Bull. Soc. Math. France 66, 210–220.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. 2. Wiley, New York.Google Scholar
Orey, S. (1971) Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities. Van Nostrand Reinhold, London.Google Scholar