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 $\alpha \gt 1$.
Citation
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
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