General approach to the maximum of a random walk under heavy upload
Teoriâ veroâtnostej i ee primeneniâ, Tome 55 (2010) no. 2, pp. 335-344 Cet article a éte moissonné depuis la source Math-Net.Ru

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V. I. Vakhtel'; V. V. Shneer. General approach to the maximum of a random walk under heavy upload. Teoriâ veroâtnostej i ee primeneniâ, Tome 55 (2010) no. 2, pp. 335-344. http://geodesic.mathdoc.fr/item/TVP_2010_55_2_a5/

[1] Asmussen S., Applied Probability and Queues, Springer-Verlag, New York, 2003, 438 pp. | MR

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

[3] Boxma O. J., Cohen J. W., “Heavy-traffic analysis for the GI/G/1 queue with heavy-tailed distributions”, Queueing Syst., 33:1–3 (1999), 177–204 | DOI | MR | Zbl

[4] Cohen J. W., “Random walk with a heavy-tailed jump distribution”, Queueing Syst., 40:1 (2002), 35–73 | DOI | MR | Zbl

[5] Furrer H., Risk theory and heavy-tailed Lévy processes, PhD Thesis, ETH, Zürich, 1997

[6] Gikhman I. I., Skorokhod A. V., Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1965, 655 pp. | MR

[7] Kingman J. F. C., “The single server queue in heavy traffic”, Proc. Cambridge Philos. Soc., 57 (1961), 902–904 | DOI | MR | Zbl

[8] Kingman J. F. C., “On queues in heavy traffic”, J. Roy Statist. Soc., Ser. B, 24 (1962), 383–392 | MR | Zbl

[9] Kingman J. F. C., “The heavy traffic approximation in the theory of queues”, Proceedings of Symposium on Congestion Theory, eds. W. L. Smith and W. E. Wilkinson, University of North Carolina Press, 1965, 137–159 | MR

[10] Prokhorov Yu. V., “Perekhodnye yavleniya v vetvyaschikhsya protsessakh. I”, Litov. matem. sb., 3 (1963), 199–205

[11] Pruitt W. E., “The growth of random walks and Lévy processes”, Ann. Probab., 9:6 (1981), 948–956 | DOI | MR | Zbl

[12] Resnick S., Samorodnitsky G., “A heavy traffic limit theorem for workload processes with heavy tailed service requirements”, Management Sci., 46 (2000), 1236–1248 | DOI

[13] Sakhanenko A. I., “O perekhodnykh yavleniyakh v sluchainykh bluzhdaniyakh”, Teoriya veroyatn. i ee primen., 49:2 (2004), 382–395 | MR | Zbl

[14] Sato K.-I., Lévy Processes and Infinitely Divisible Distributions, Cambridge Univ. Press, Cambridge, 2005 | Zbl

[15] Seneta E., Pravilno menyayuschiesya funktsii, Nauka, M., 1985, 141 pp. | MR | Zbl

[16] Spitser F., Printsip sluchainogo bluzhdaniya, Mir, M., 1969, 472 pp.