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On Large Deviations of Multivariate Heavy-Tailed Random Walks

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  • Harri Nyrhinen

    (University of Helsinki)

Abstract

Let {S n ;n=1,2,…} be a random walk in R d and E(S 1)=(μ 1,…,μ d ). Let a j >μ j for j=1,…,d and A=(a 1,∞)×⋅⋅⋅×(a d ,∞). We are interested in the probability P(S n /n∈A) for large n in the case where the components of S 1 are heavy tailed. An objective is to associate an exact power with the aforementioned probability. We also derive sharper asymptotic bounds for the probability and show that in essence, the occurrence of the event {S n /n∈A} is caused by large single increments of the components in a specific way.

Suggested Citation

  • Harri Nyrhinen, 2009. "On Large Deviations of Multivariate Heavy-Tailed Random Walks," Journal of Theoretical Probability, Springer, vol. 22(1), pages 1-17, March.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:1:d:10.1007_s10959-008-0194-2
    DOI: 10.1007/s10959-008-0194-2
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    References listed on IDEAS

    as
    1. Y. Hu & H. Nyrhinen, 2004. "Large Deviations View Points for Heavy-Tailed Random Walks," Journal of Theoretical Probability, Springer, vol. 17(3), pages 761-768, July.
    2. Gantert, Nina, 2000. "A note on logarithmic tail asymptotics and mixing," Statistics & Probability Letters, Elsevier, vol. 49(2), pages 113-118, August.
    3. Asmussen, Søren & Klüppelberg, Claudia, 1996. "Large deviations results for subexponential tails, with applications to insurance risk," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 103-125, November.
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