Large Deviations View Points for Heavy-Tailed Random Walks

Y. Hu () and H. Nyrhinen ()
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Y. Hu: Wuhan University
H. Nyrhinen: University of Helsinki

Journal of Theoretical Probability, 2004, vol. 17, issue 3, 761-768

Abstract: Abstract Let X 1, X 2,... be a sequence of i.i.d. non-negative random variables with heavy tails. W e study logarithmic asymptotics for the distributions of the partial sums S n = X 1 + ··· + X n . Our main interest is in the crude estimates P(S n > n x ) ≈ n −αx + 1 for appropriate values of x where α is a specific parameter. The related conjecture proposed by Gantert (Stat. Probab. Lett. 49, 113–118) is investigated.

Keywords: Logarithmic tail asymptotics; large deviations; heavy tails (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (3)

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DOI: 10.1023/B:JOTP.0000040298.43712.e8

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