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 
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/
@article{VNGU_2008_8_1_a4,
     author = {V. I. Lotov},
     title = {On the asymptotics of moments for the supremum of a trajectory for random walks with small drift},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {51--58},
     year = {2008},
     volume = {8},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2008_8_1_a4/}
}
TY  - JOUR
AU  - V. I. Lotov
TI  - On the asymptotics of moments for the supremum of a trajectory for random walks with small drift
JO  - Sibirskij žurnal čistoj i prikladnoj matematiki
PY  - 2008
SP  - 51
EP  - 58
VL  - 8
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VNGU_2008_8_1_a4/
LA  - ru
ID  - VNGU_2008_8_1_a4
ER  - 
%0 Journal Article
%A V. I. Lotov
%T On the asymptotics of moments for the supremum of a trajectory for random walks with small drift
%J Sibirskij žurnal čistoj i prikladnoj matematiki
%D 2008
%P 51-58
%V 8
%N 1
%U http://geodesic.mathdoc.fr/item/VNGU_2008_8_1_a4/
%G ru
%F VNGU_2008_8_1_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Kingman J. F. C., “On Queues in Heavy Traffic”, J. Roy. Stat. Soc. Ser. B, 24:2 (1962), 383–392 | MR | Zbl

[2] Prokhorov Yu. V., “Perekhodnye yavleniya v protsessakh massovogo obsluzhivaniya”, Lit. mat. sb., 1 (1963), 199–206 | MR | Zbl

[3] Cohen J. W., “Random Walk with a Heavy-Tailed Jump Distribution”, Queueing Syst., 40:1 (2002), 35–73 | DOI | MR | Zbl

[4] Borovkov A. A., “Perekhodnye yavleniya dlya sluchainykh bluzhdanii s raznoraspredelennymi skachkami, imeyuschimi beskonechnye dispersii”, Teoriya veroyatnostei i ee primeneniya, 50:2 (2005), 224–240 | DOI

[5] Korshunov D. A., “Perekhodnye yavleniya dlya veschestvennoznachnykh tsepei Markova”, Tr. IM SO AN, 20 (1993), 116–161 | MR | Zbl

[6] Kalashnikov V., Geometric Sums: Bounds for Rare Events with Applications, Kluwer Academic Publishers, Dordrecht, 1997 | MR | Zbl

[7] Asmussen S., Applied Probability and Queues, Springer, N.Y., 2003 | MR | Zbl

[8] Shprenger A. V., Asimptotika srednego vremeni ozhidaniya v odnokanalnoi sisteme massovogo obsluzhivaniya v usloviyakh bolshoi nagruzki, Dipl. rabota (nauch. ruk. D. A. Korshunov), Novosibirskii gosudarstvennyi universitet. MMF, 2007

[9] Borovkov A. A., Teoriya veroyatnostei, Nauka, M., 1986 | MR | Zbl

[10] Chang J. T., “On Moments of the First Ladder Height of Random Walks with Small Drift”, Ann. Appl. Probab., 2:3 (1992), 714–736 | DOI | MR

[11] Gut A., Stopped Random Walks. Limit Theorems and Applications, Springer, 1988 | Zbl

[12] Siegmund D., “Corrected Diffusion Approximations in Certain Random Walk Problems”, Adv. Appl. Probab., 11 (1979), 701–719 | DOI | MR | Zbl

[13] Siegmund D., Sequential Analysis: Tests and Confidence Intervals, Springer, N.Y., 1985 | MR | Zbl