A comparison of random walks in dependent random environments

Willem R.W. Scheinhardt, Dirk P. Kroese

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Abstract

Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the actual evaluation of various characteristics of such processes has received relatively little attention. This paper develops new methodology for the exact computation of the drift in such models. Focusing on random walks in dependent random environments, including $k$-dependent and moving average environments, we show how the drift can be characterized and found using Perron-Frobenius theory. We compare random walks in various dependent environments and show that their drift behavior can differ signicantly.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente
Number of pages20
Publication statusPublished - 16 Jan 2015

Publication series

NameMemorandum
PublisherUniversity of Twente, Department of Applied Mathematics
No.2041
ISSN (Print)1874-4850

Keywords

  • Dependent random environment
  • Random walk
  • Drift
  • Perron-Frobenius eigenvalue
  • MSC-60K37
  • MSC-82B41

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