Geodesic
On the convergence rate in ``the exact asymptotics'' for random variables with a stable distribution
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 259-275

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In the note we present the conditions under which relations of the type $$ \lim\limits_{\varepsilon\searrow 0}\left(\sum\limits_{n\ge 1} r(n) \mathbf{P}(Y_\alpha\ge f(\varepsilon g(n))) - \nu(\varepsilon) \right) = C $$ hold, where a random variable $Y_\alpha$ has a stable distribution, $C$ is a constant, and non-negative functions $r$, $f$ and $g$ satisfy certain conditions. The obtained results allow to make more precise and to complement results, related to the convergence rate in the so called “exact asymptotics”. 
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     author = {L. V. Rozovsky},
     title = {On the convergence rate in ``the exact asymptotics'' for random variables with a stable distribution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {259--275},
     publisher = {mathdoc},
     volume = {501},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a16/}
}
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L. V. Rozovsky. On the convergence rate in ``the exact asymptotics'' for random variables with a stable distribution. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 30, Tome 501 (2021), pp. 259-275. http://geodesic.mathdoc.fr/item/ZNSL_2021_501_a16/