FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2002, VOLUME 8, NUMBER 3, PAGES 911-920
M. S. Sgibnev
Abstract
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Let $\{S_{k}\}$ be a random walk drifting to $-\infty$ .
The exact asymptotic behaviour of
$\sum\limits_{k=1}^{\infty}\mathsf P (S_{k}\geq x)$
is considered under the following moment conditions:
for some $\gamma>0$ ,
$\mathsf E e^{\gamma S_{1}}=1$ ,
$\mathsf E |S_{1}|e^{\gamma S_{1}}<\infty$
and, in general,
$\mathsf E S_{1}^{2}e^{\gamma S_{1}}=\infty$ .
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Last modified: February 17, 2003