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Asymptotic formulas for probabilities of
large deviations of ladder heights
Sergey V. Nagaev Sobolev Institute of Mathematics, 4, Koptyug Pr., Novosibirsk 630090, Russia
Аннотация:
Asymptotic formulas for large-deviation probabilities of a ladder height in a random
walk generated by a sequence of sums of i.i.d. random variables are deduced.
Two cases are considered:
a) the distribution $F(x)$ of summands is normal with a zero mean.
b) $F(x)$ belongs to the domain of the normal attraction of a stable law with
the exponent $0 <\alpha< 1.$
The method of Laplace transforms is applied in proofs.
Ключевые слова:
Characteristic function, harmonic renewal measure, Karamata’s criterion,
ladder height, Laplace transform, slowly varying function, Spitzer series, Tauberian theorem.
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Тип публикации:
Статья
MSC: 60F10
Язык публикации: английский
Образец цитирования:
Sergey V. Nagaev, “Asymptotic formulas for probabilities of
large deviations of ladder heights”, Theory Stoch. Process., 14(30):1 (2008), 100–116
Цитирование в формате AMSBIB
\RBibitem{Nag08}
\by Sergey~V.~Nagaev
\paper Asymptotic formulas for probabilities of
large deviations of ladder heights
\jour Theory Stoch. Process.
\yr 2008
\vol 14(30)
\issue 1
\pages 100--116
\mathnet{http://mi.mathnet.ru/thsp134}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2479711}
\zmath{https://zbmath.org/?q=an:1199.60064}
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