Geodesic
On the convergence rate in precise asymptotics
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 1, pp. 57-74

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We study some aspects of estimation of the convergence rate in the so-called “exact asymptotics.” In particular, we obtain asymptotic expansions in powers of $\varepsilon$ of sums of the form $\sum_{n\ge 1} n^s\,\mathbf P(\xi_{\alpha}> \varepsilon n^{\delta})$, where a random variable $\xi_{\alpha}$ has a stable distribution with an exponent $\alpha\in (0, 2]$, $\delta>0$, $s\in \mathbf R$.
Mots-clés : convergence rates
Keywords: precise asymptotics, complete convergence. 
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     author = {L. V. Rozovskii},
     title = {On the convergence rate in precise asymptotics},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {57--74},
     publisher = {mathdoc},
     volume = {68},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2023_68_1_a3/}
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L. V. Rozovskii. On the convergence rate in precise asymptotics. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 1, pp. 57-74. http://geodesic.mathdoc.fr/item/TVP_2023_68_1_a3/