Geodesic
On the mean value of the ladder epoch for random walks with a small drift
Izvestiya. Mathematics , Tome 70 (2006) no. 6, pp. 1225-1232.

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In this paper, we prove theorems on the asymptotic behaviour of the mean value of the time at which the non-negative half-axis is first attained for a random walk whose drift tends to zero. It is assumed that the distribution of jumps of the random walk belongs to the domain of attraction of a stable law with exponent $\alpha\in(1,2)$. 
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V. I. Lotov. On the mean value of the ladder epoch for random walks with a small drift. Izvestiya. Mathematics , Tome 70 (2006) no. 6, pp. 1225-1232. http://geodesic.mathdoc.fr/item/IM2_2006_70_6_a5/

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