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Numerically Optimized Markovian Coupling and Mixing in One-Dimensional Maps

Part of: Markov processes

Published online by Cambridge University Press:  21 December 2009

Kalvis M. Jansons  and
Paul D. Metcalfe
Kalvis M. Jansons
Affiliation:
Department of Mathematics, University College London, Gower Street, LondonWC1E 6BT. E-mail: coupling@kalvis.com
Paul D. Metcalfe
Affiliation:
Cyprotex Discovery Ltd., 15 Beech Lane, Macclesfield SK10 2DR.
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Abstract

Algorithms are introduced that produce optimal Markovian couplings for large finite-state-space discrete-time Markov chains with sparse transition matrices; these algorithms are applied to some toy models motivated by fluid-dynamical mixing problems at high Peclét number. An alternative definition of the time-scale of a mixing process is suggested. Finally, these algorithms are applied to the problem of coupling diffusion processes in an acute-angled triangle, and some of the simplifications that occur in continuum coupling problems are discussed.

MSC classification

Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J22: Computational methods in Markov chains
Type
Research Article
Information
Mathematika , Volume 54 , Issue 1-2 , December 2007 , pp. 161 - 181
Copyright
Copyright © University College London 2007

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