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Conservative and Semiconservative Random Walks: Recurrence and Transience

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  • Vyacheslav M. Abramov

    (Monash University
    Royal Melbourne Institute of Technology)

Abstract

In the present paper, we define conservative and semiconservative random walks in $$\mathbb {Z}^d$$ Z d and study various families of random walks. The family of symmetric random walks is one of the families of conservative random walks, and simple (Pólya) random walks are their representatives. The classification of random walks given in the present paper enables us to provide a new approach to random walks in $$\mathbb {Z}^d$$ Z d by reduction to birth-and-death processes. We construct nontrivial examples of recurrent random walks in $$\mathbb {Z}^d$$ Z d for any $$d\ge 3$$ d ≥ 3 and transient random walks in $$\mathbb {Z}^2$$ Z 2 .

Suggested Citation

  • Vyacheslav M. Abramov, 2018. "Conservative and Semiconservative Random Walks: Recurrence and Transience," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1900-1922, September.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0747-3
    DOI: 10.1007/s10959-017-0747-3
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    References listed on IDEAS

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    1. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
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    Cited by:

    1. Vyacheslav M. Abramov, 2023. "Crossings States and Sets of States in Random Walks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-34, March.

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