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A coupling proof of weak convergence

Published online by Cambridge University Press:  14 July 2016

Peter Guttorp ,
Reg Kulperger  and
Richard Lockhart
Peter Guttorp*
Affiliation:
University of Washington
Reg Kulperger*
Affiliation:
University of Western Ontario
Richard Lockhart*
Affiliation:
Simon Fraser University
*
∗Postal address: Department of Statistics, University of Washington, Seattle, WA 98195, USA.
∗∗Postal address: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, Ont., Canada.
∗∗∗Postal address: Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada V5A 1S6.
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Abstract

Weak convergence to reflected Brownian motion is deduced for certain upwardly drifting random walks by coupling them to a simple reflected random walk. The argument is quite elementary, and also gives the right conditions on the drift. A similar argument works for a corresponding continuous-time problem.

Keywords

RANDOM WALKDIFFUSIONS WITH DRIFT
Type
Short Communications
Information
Journal of Applied Probability , Volume 22 , Issue 2 , June 1985 , pp. 447 - 453
Copyright
Copyright © Applied Probability Trust 1985 

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References

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