FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2002, VOLUME 8, NUMBER 3, PAGES 911-920

**Exact asymptotic behaviour of the renewal measure in the "critical"
case**

M. S. Sgibnev

Abstract

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Let $\{S$_{k}} be a random walk drifting to
$$-¥.
The exact asymptotic behaviour of
$$S_{k=1}^{¥}P (S_{k} ³ x)
is considered under the following moment conditions:
for some $$g
> 0,
$E\; e$g S_{1} = 1,
$E\; |S$_{1}| e^{g S1} <
¥
and, in general,
$E\; S$_{1}^{2}
e^{g S1} =
¥.

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published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k02/k023/k02316h.htm

Last modified: September 26, 2004