Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T04:43:47.478Z Has data issue: false hasContentIssue false
  • English
  • Français

On coupling of random walks and renewal processes

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Torgny Lindvall  and
L. C. G. Rogers
Torgny Lindvall*
Affiliation:
University of Göteborg
L. C. G. Rogers*
Affiliation:
University of Bath
*
∗Postal address: Department of Mathematics, University of Göteborg, 41296 Göteborg, Sweden. E-mail: [email protected]
∗∗Postal address: School of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 2AY, U.K. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.

Keywords

ERGODICITYRANDOM WALKCOUPLINGBLACKWELL'S RENEWAL THEOREM

MSC classification

Secondary: 60K05: Renewal theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 122 - 126
Copyright
Copyright © Applied Probability Trust 1996 

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] Kerstan, J. and Matthes, K. (1968) Gleichverteilungseigenschaften von Faltungen von Verteilungsgesetzen auf lokalkompakten abelschen Gruppen. I. Math. Nachr. 37, 267–312.Google Scholar
[2] Krengel, U. (1985) Ergodic Theorems. de Gruyter, Berlin.Google Scholar
[3] Lindvall, T. (1992) Lectures on the Coupling Method. Wiley, New York.Google Scholar
[4] Revuz, D. (1984) Markov Chains. 2nd edn. North-Holland, Amsterdam.Google Scholar