On Large Deviations of Multivariate Heavy-Tailed Random Walks

Harri Nyrhinen ()
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Harri Nyrhinen: University of Helsinki

Journal of Theoretical Probability, 2009, vol. 22, issue 1, 1-17

Abstract: 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.

Keywords: Heavy tail; Large deviation; Random walk; 60F10 (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10959-008-0194-2

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