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A comparison of random walks in dependent random environments

Part of: Special processes Equilibrium statistical mechanics Stochastic processes

Published online by Cambridge University Press:  24 March 2016

Werner R. W. Scheinhardt  and
Dirk P. Kroese
Werner R. W. Scheinhardt*
Affiliation:
University of Twente
Dirk P. Kroese*
Affiliation:
The University of Queensland
*
* Postal address: Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands. Email address: [email protected]
** Postal address: School of Mathematics and Physics, The University of Queensland, St Lucia, Brisbane, 4072, Australia. Email address: [email protected]
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Abstract

We provide exact computations for the drift of random walks in dependent random environments, including k-dependent and moving average environments. We show how the drift can be characterized and evaluated using Perron–Frobenius theory. Comparing random walks in various dependent environments, we demonstrate that their drifts can exhibit interesting behavior that depends significantly on the dependency structure of the random environment.

Keywords

Random walkdependent random environmentdriftPerron–Frobenius eigenvalue

MSC classification

Primary: 60K37: Processes in random environments 60G50: Sums of independent random variables; random walks
Secondary: 82B41: Random walks, random surfaces, lattice animals, etc.
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 1 , March 2016 , pp. 199 - 214
Copyright
Copyright © Applied Probability Trust 2016 

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