Geodesic
Precise asymptotics over a small
Teoriâ slučajnyh processov, Tome 13 (2007) no. 1, pp. 44-56.

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We obtain the asymptotics of the series $$ \sum^\infty_{k=1}w_k({\mathbf P}(|S_k|\geq\varepsilon_k) $$are par as $\varepsilon\downarrow0,$ where $S_k$ tial sums of independent and identically distributed random variables in the domain of attraction of a non-degenerate stable law, $w$ and $\varepsilon$ are regularly varying functions (in Karamata’s sense).
Keywords: Spitzer series, large deviations, stable laws, regularly varying functions. 
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V. V. Buldygin; O. I. Klesov; J. G. Steinebach. Precise asymptotics over a small. Teoriâ slučajnyh processov, Tome 13 (2007) no. 1, pp. 44-56. http://geodesic.mathdoc.fr/item/THSP_2007_13_1_a4/

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