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Optimal Co-Adapted Coupling for the Symmetric Random Walk on the Hypercube

Part of: Stochastic systems and control Markov processes

Published online by Cambridge University Press:  14 July 2016

Stephen Connor  and
Saul Jacka
Stephen Connor*
Affiliation:
University of Warwick
Saul Jacka*
Affiliation:
University of Warwick
*
∗Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
∗Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
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Abstract

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Let X and Y be two simple symmetric continuous-time random walks on the vertices of the n-dimensional hypercube, Z2n. We consider the class of co-adapted couplings of these processes, and describe an intuitive coupling which is shown to be the fastest in this class.

Keywords

Optimal couplingco-adaptedstochastic minimumhypercube

MSC classification

Secondary: 93E20: Optimal stochastic control 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 3 , September 2008 , pp. 703 - 713
Copyright
Copyright © Applied Probability Trust 2008 

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