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A comparison of random walks in dependent random environments

  • Werner R. W. Scheinhardt (a1) and Dirk P. Kroese (a2)

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.

Corresponding author
* Postal address: Department of Applied Mathematics, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands. Email address:
** Postal address: School of Mathematics and Physics, The University of Queensland, St Lucia, Brisbane, 4072, Australia. Email address:
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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