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January 2006 The asymptotic behavior over a small parameter of a series of large deviation probabilities weighted with the Dirichlet divisors function
Karl-Heinz Indlekofer, Oleg Klesov
Funct. Approx. Comment. Math. 35: 117-131 (January 2006). DOI: 10.7169/facm/1229442620

Abstract

We obtain the precise asymptotics of the series $$\sum_{k=1}^\infty \frac {d_k}k \mathtt{P}(|S_k| \ge \varepsilon k)$$ as $\varepsilon \downarrow 0$ where $S_k$ are partial sums of independent identically distributed random variables attracted to a stable law of index $\alpha \gt 1$.

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Karl-Heinz Indlekofer. Oleg Klesov. "The asymptotic behavior over a small parameter of a series of large deviation probabilities weighted with the Dirichlet divisors function." Funct. Approx. Comment. Math. 35 117 - 131, January 2006. https://doi.org/10.7169/facm/1229442620

Information

Published: January 2006
First available in Project Euclid: 16 December 2008

zbMATH: 1116.60009
MathSciNet: MR2271610
Digital Object Identifier: 10.7169/facm/1229442620

Subjects:
Primary: 60F05, 60G50
Secondary: 60G15

Rights: Copyright © 2006 Adam Mickiewicz University

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Vol.35 • January 2006
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