Advances in Applied Probability

A comparison of random walks in dependent random environments

Werner R. W. Scheinhardt and Dirk P. Kroese

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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.

Article information

Source
Adv. in Appl. Probab., Volume 48, Number 1 (2016), 199-214.

Dates
First available in Project Euclid: 8 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.aap/1457466162

Mathematical Reviews number (MathSciNet)
MR3473574

Zentralblatt MATH identifier
1337.60251

Subjects
Primary: 60K37: Processes in random environments 60G50: Sums of independent random variables; random walks
Secondary: 82B41: Random walks, random surfaces, lattice animals, etc. [See also 60G50, 82C41]

Keywords
Random walk dependent random environment drift Perron-Frobenius eigenvalue

Citation

Scheinhardt, Werner R. W.; Kroese, Dirk P. A comparison of random walks in dependent random environments. Adv. in Appl. Probab. 48 (2016), no. 1, 199--214. https://projecteuclid.org/euclid.aap/1457466162


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