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An interesting random walk on the non-negative integers

Published online by Cambridge University Press:  14 July 2016

Marcel F. Neuts
Marcel F. Neuts*
Affiliation:
University of Arizona
*
∗ Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ 85721, USA.
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Abstract

A particular random walk on the integers leads to a new, tractable Markov chain. Of the stationary probabilities, we discuss the existence, some analytic properties and a factorization which leads to an algorithmic procedure for their numerical computation. We also consider the positive recurrence of some variants which each call for different mathematical arguments. Analogous results are derived for a continuous version on the positive reals.

Keywords

MARKOV CHAINSSTATIONARY PROBABILITIESPHASE-TYPE DISTRIBUTIONSALGORITHMIC PROBABILITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 1 , March 1994 , pp. 48 - 58
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

This research was supported in part by Grant Nr. DDM-8915235 from the National Science Foundation.

References

[1] Fuhrmann, S. W. and Cooper, R. B. (1985) Stochastic decompositions in the M/G/1 queue with generalized vacations. Operat. Res. 33, 1117–1129.Google Scholar
[2] Neuts, M. F. (1981) Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Baltimore.Google Scholar
[3] Neuts, M. F. (1991) Probabilistic modelling requires a certain imagination. In Proceedings of the Third International Conference on Teaching Statistics (ICOTS 3), August 19-24, 1990, Dunedin, New Zealand, ed. Vere-Jones, David, Vol. 2, pp. 122–131.Google Scholar