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On coupling of random walks and renewal processes

Published online by Cambridge University Press:  14 July 2016

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]

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.

MSC classification

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1996 

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References

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