Geodesic
On the asymptotics of moments for the supremum of a trajectory for random walks with small drift
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 1, pp. 51-58

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Under Cramér-type conditions, we obtain four terms of asymptotic expansions for the first two moments for the supremum of a trajectory for random walk whose drift vanishes. 
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     author = {V. I. Lotov},
     title = {On the asymptotics of moments for the supremum of a trajectory for random walks with small drift},
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V. I. Lotov. On the asymptotics of moments for the supremum of a trajectory for random walks with small drift. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 1, pp. 51-58. http://geodesic.mathdoc.fr/item/VNGU_2008_8_1_a4/