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Moderate and Small Deviations for the Ranges of One-Dimensional Random Walks

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  • Xia Chen

    (University of Tennessee)

Abstract

We establish moderate and small deviations for the ranges of integer valued random walks. Our theorems apply to the limsup and the liminf laws of the iterated logarithm.

Suggested Citation

  • Xia Chen, 2006. "Moderate and Small Deviations for the Ranges of One-Dimensional Random Walks," Journal of Theoretical Probability, Springer, vol. 19(3), pages 721-739, December.
    • Handle: RePEc:spr:jotpro:v:19:y:2006:i:3:d:10.1007_s10959-006-0032-3
    DOI: 10.1007/s10959-006-0032-3
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    References listed on IDEAS

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    1. Hamana, Yuji, 1998. "An almost sure invariance principle for the range of random walks," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 131-143, November.
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    Cited by:

    1. Cygan, Wojciech & Sandrić, Nikola & Šebek, Stjepan, 2023. "Invariance principle for the capacity and the cardinality of the range of stable random walks," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 61-84.

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