Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T00:36:12.697Z Has data issue: false hasContentIssue false
  • English
  • Français

On Coupling of continuous-time renewal 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, S-412 96 Göteborg, Sweden.
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper shows how the coupling method applies to renewal theory in continuous time. Old and new rate results for tendency towards equilibrium and forgetfulness of initial delay are obtained. The coupling approach also provides a new way of analysing the asymptotics of functions of renewal processes which avoids the route via a renewal equation.

Keywords

RENEWAL PROCESSESCOUPLINGRATE RESULTS
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 82 - 89
Copyright
Copyright © Applied Probability Trust 1982 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Arjas, E., Nummelin, E. and Tweedie, R. L. (1978) Uniform limit theorems for non-singular renewal and Markov renewal processes. J. Appl. Prob. 15, 112–125.CrossRefGoogle Scholar
[2] Athreya, K. B. and Ney, P. (1978) A new approach to the limit theory of recurrent Markov chains. Trans. Amer. Math. Soc. 245, 493–501.CrossRefGoogle Scholar
[3] Jagers, P. (1974) Aspects of random measures and point processes. In Advances in Probability, Vol. 3, ed. Ney, P. and Port, S.. Dekker, New York.Google Scholar
[4] Lindvall, T. (1979) On coupling of discrete renewal processes. Z. Wahrscheinlichkeitsth. 48, 57–70.CrossRefGoogle Scholar
[5] Ney, P. (1981) A refinement of the coupling method in renewal theory. Stoch. Proc. Appl. 11, 11–26.CrossRefGoogle Scholar
[6] Nummelin, E. (1978) A splitting technique for Harris recurrent Markov chains. Z. Wahrscheinlichkeitsth. 43, 309–318.CrossRefGoogle Scholar
[7] Pitman, J. W. (1974) Uniform rates of convergence for Markov chain transition probabilities. Z. Wahrscheinlichkeitsth. 29, 193–227.CrossRefGoogle Scholar
[8] Stone, C. J. (1966) On absolutely continuous components and renewal theory. Ann. Math. Statist. 37, 271–275.CrossRefGoogle Scholar