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Multidimensional random walk with reflections

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  • Kloas, Judith
  • Woess, Wolfgang

Abstract

Reflected random walk in higher dimension arises from an ordinary random walk (sum of i.i.d. random variables): whenever one of the reflecting coordinates becomes negative, its sign is changed, and the process continues from that modified position. One-dimensional reflected random walk is quite well understood from work in 7 decades, but the multidimensional model presents several new difficulties. Here we investigate recurrence questions.

Suggested Citation

  • Kloas, Judith & Woess, Wolfgang, 2019. "Multidimensional random walk with reflections," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 336-354.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:1:p:336-354
    DOI: 10.1016/j.spa.2018.03.003
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    References listed on IDEAS

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    1. Kemperman, J. H. B., 1974. "The oscillating random walk," Stochastic Processes and their Applications, Elsevier, vol. 2(1), pages 1-29, January.
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