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• W2036291212 abstract "We study limiting distributions of exponential sums as t→∞, N→∞, where (X i ) are i.i.d. random variables. Two cases are considered: (A) ess sup X i = 0 and (B) ess sup X i = ∞. We assume that the function h(x)= -log P{X i >x} (case B) or h(x) = -log P {X i >-1/x} (case A) is regularly varying at ∞ with index 1 < ϱ <∞ (case B) or 0 < ϱ < ∞ (case A). The appropriate growth scale of N relative to t is of the form , where the rate function H0(t) is a certain asymptotic version of the function (case B) or (case A). We have found two critical points, λ1<λ2, below which the Law of Large Numbers and the Central Limit Theorem, respectively, break down. For 0 < λ < λ2, under the slightly stronger condition of normalized regular variation of h we prove that the limit laws are stable, with characteristic exponent α = α (ϱ, λ) ∈ (0,2) and skewness parameter β ≡ 1." @default.
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• W2036291212 date "2005-02-10" @default.
• W2036291212 modified "2023-09-26" @default.
• W2036291212 title "Limit theorems for sums of random exponentials" @default.
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• W2036291212 doi "https://doi.org/10.1007/s00440-004-0406-3" @default.
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