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A note on coupling of birth and death processes

Published online by Cambridge University Press:  14 July 2016

Torgny Lindvall
Torgny Lindvall*
Affiliation:
University of Göteborg
*
∗ Postal address: Department of Mathematics, Chalmers University of Technology and University of Göteborg, Fack, S–402 20 Göteborg, Sweden.
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Abstract

The purpose of this note is to show how well the coupling device is fitted for use in the study of birth and death process asymptotics: known achievements get new proofs, and new results on rate of ‘forgetfulness of initial state' and stochastic domination are established.

Keywords

COUPLINGSBIRTH AND DEATH PROCESSESRATE RESULTSSTOCHASTIC DOMINATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 505 - 512
Copyright
Copyright © Applied Probability Trust 1979 

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References

[1] Doeblin, W. (1938) Exposé de la théorie des chaînes simple constantes de Markov a un nombre fini d'états. Rev. Math, de l'Union Interbalkanique 2, 77–105.Google Scholar
[2] Feller, W. (1968) An Introduction to Probability Theory and its Applications Vol. I, 3rd edn. Wiley, New York.Google Scholar
[3] Griffeath, D. (1975) A maximal coupling for Markov chains. Z. Wahrscheinlichkeitsth. 31, 95–106.Google Scholar
[4] Griffeath, D. (1976) Coupling Methods for Markov Processes. Thesis, Cornell University.Google Scholar
[5] Harris, T. E. (1952) First passage and recurrence distributions. Trans. Amer. Math. Soc. 73, 471–486.Google Scholar
[6] Kamae, T., Krengel, U. and O'Brien, G. L. (1977) Stochastic inequalities on partially ordered spaces. Ann. Prob. 5, 899–912.Google Scholar
[7] Karlin, S. and Mcgregor, J. L. (1957) The classification of birth and death processes. Trans. Amer. Math. Soc. 86, 366–400.Google Scholar
[8] Lindvall, T. (1977) A probabilistic proof of Blackwell's renewal theorem. Ann. Prob. 5, 482–485.Google Scholar
[9] Pitman, J. W. (1974) Uniform rates of convergence for Markov chain transition probabilities. Z. Wahrscheinlichkeitsth. 29, 193–227.Google Scholar
[10] Pitman, J. W. (1976) On coupling of Markov chains. Z. Wahrscheinlichkeitsth. 35, 315–322.Google Scholar