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Some Limit Theorems for Heights of Random Walks on a Spider

Author

Listed:
  • Endre Csáki

    (Hungarian Academy of Sciences)

  • Miklós Csörgő

    (Carleton University)

  • Antónia Földes

    (College of Staten Island, CUNY)

  • Pál Révész

    (Technische Universität Wien)

Abstract

A simple random walk is considered on a spider that is a collection of half lines (we call them legs) joined at the origin. We establish a strong approximation of this random walk by the so-called Brownian spider. Transition probabilities are studied, and for a fixed number of legs we investigate how high the walker and the Brownian motion can go on the legs in n steps. The heights on the legs are also investigated when the number of legs goes to infinity.

Suggested Citation

  • Endre Csáki & Miklós Csörgő & Antónia Földes & Pál Révész, 2016. "Some Limit Theorems for Heights of Random Walks on a Spider," Journal of Theoretical Probability, Springer, vol. 29(4), pages 1685-1709, December.
    • Handle: RePEc:spr:jotpro:v:29:y:2016:i:4:d:10.1007_s10959-015-0626-8
    DOI: 10.1007/s10959-015-0626-8
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    References listed on IDEAS

    as
    1. Endre Csáki & Yueyun Hu, 2001. "Asymptotic Properties of Ranked Heights in Brownian Excursions," Journal of Theoretical Probability, Springer, vol. 14(1), pages 77-96, January.
    2. Vassilis G. Papanicolaou & Effie G. Papageorgiou & Dimitris C. Lepipas, 2012. "Random Motion on Simple Graphs," Methodology and Computing in Applied Probability, Springer, vol. 14(2), pages 285-297, June.
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