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.
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Hu, Y., Nyrhinen, H. Large Deviations View Points for Heavy-Tailed Random Walks. Journal of Theoretical Probability 17, 761–768 (2004). https://doi.org/10.1023/B:JOTP.0000040298.43712.e8
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DOI: https://doi.org/10.1023/B:JOTP.0000040298.43712.e8