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Theory of Probability and Mathematical Statistics

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The mean coupling time for independent discrete renewal processes


Authors: M. V. Kartashov and V. V. Golomozyĭ
Translated by: O. I. Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 84 (2011).
Journal: Theor. Probability and Math. Statist. 84 (2012), 79-86
MSC (2010): Primary 60J45; Secondary 60A05, 60K05
DOI: https://doi.org/10.1090/S0094-9000-2012-00855-7
Published electronically: July 31, 2012
MathSciNet review: 2857418
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Abstract: We consider two independent renewal processes with discrete and, in general, nonidentical distributions of interarrival times. The mean coupling time is estimated via the first two moments of these distributions.

References [Enhancements On Off] (What's this?)

  • 1. T. Lindvall, Lectures on the Coupling Method, Wiley, New York, 1991. MR 1180522 (94c:60002)
  • 2. N. V. Kartashov, Strong Stable Markov Chains, VSP/TViMS, Utrecht/Kiev, The Netherlands/Ukraine, 1996. MR 1451375 (99e:60150)
  • 3. W. Feller, An Introduction to Probability Theory and its Applications, vol. 1, John Wiley & Sons, New York, 1966. MR 0210154 (35:1048)
  • 4. D. J. Daley, Tight bounds for the renewal function of a random walk, Ann. Probab. 8 (1980), no. 3, 615-621. MR 573298 (81e:60094)

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Additional Information

M. V. Kartashov
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kiev 03127, Ukraine
Email: nkartashov@skif.com.ua

V. V. Golomozyĭ
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 4E, Kiev 03127, Ukraine

DOI: https://doi.org/10.1090/S0094-9000-2012-00855-7
Keywords: Renewal theory, renewal sequences, coupling method, coupling time
Received by editor(s): December 17, 2010
Published electronically: July 31, 2012
Article copyright: © Copyright 2012 American Mathematical Society

American Mathematical Society