The mean coupling time for independent discrete renewal processes
Authors:
M. V. Kartashov and V. V. Golomozyĭ
Translated by:
O. I. Klesov
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
Full-text PDF Free Access
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Additional Information
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
- Torgny Lindvall, Lectures on the coupling method, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1992. A Wiley-Interscience Publication. MR 1180522
- N. V. Kartashov, Strong stable Markov chains, VSP, Utrecht; TBiMC Scientific Publishers, Kiev, 1996. MR 1451375
- William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
- D. J. Daley, Tight bounds for the renewal function of a random walk, Ann. Probab. 8 (1980), no. 3, 615–621. MR 573298
References
- T. Lindvall, Lectures on the Coupling Method, Wiley, New York, 1991. MR 1180522 (94c:60002)
- N. V. Kartashov, Strong Stable Markov Chains, VSP/TViMS, Utrecht/Kiev, The Netherlands/Ukraine, 1996. MR 1451375 (99e:60150)
- W. Feller, An Introduction to Probability Theory and its Applications, vol. 1, John Wiley & Sons, New York, 1966. MR 0210154 (35:1048)
- 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
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
