Translator Disclaimer
December 2013 Optimal coadapted coupling for a random walk on the hyper-complete graph
Stephen Connor
Author Affiliations +
J. Appl. Probab. 50(4): 1117-1130 (December 2013). DOI: 10.1239/jap/1389370103

Abstract

The problem of constructing an optimal coadapted coupling for a pair of symmetric random walks on Z2d was considered by Connor and Jacka (2008), and the existence of a coupling which is stochastically fastest in the class of all such coadapted couplings was demonstrated. In this paper we show how to generalise this construction to an optimal coadapted coupling for the continuous-time symmetric random walk on Knd, where Kn is the complete graph with n vertices. Moreover, we show that although this coupling is not maximal for any n (i.e. it does not achieve equality in the coupling inequality), it does tend to a maximal coupling as n → ∞.

Citation

Download Citation

Stephen Connor. "Optimal coadapted coupling for a random walk on the hyper-complete graph." J. Appl. Probab. 50 (4) 1117 - 1130, December 2013. https://doi.org/10.1239/jap/1389370103

Information

Published: December 2013
First available in Project Euclid: 10 January 2014

zbMATH: 1283.93309
MathSciNet: MR3161377
Digital Object Identifier: 10.1239/jap/1389370103

Subjects:
Primary: 93E20
Secondary: 60J27

Keywords: coadapted , Cutoff phenomenon , optimal coupling , Random walk on a group , Stochastic control

Rights: Copyright © 2013 Applied Probability Trust

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.50 • No. 4 • December 2013
Back to Top