Geodesic
Exact asymptotics for the instant of crossing a curved boundary by an asymptotically stable random walk
Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 3, pp. 459-481 Cet article a éte moissonné depuis la source Math-Net.Ru

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     author = {V. I. Vakhtel' and D. \`E. Denisov},
     title = {Exact asymptotics for the instant of crossing a curved boundary by an asymptotically stable random walk},
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V. I. Vakhtel'; D. È. Denisov. Exact asymptotics for the instant of crossing a curved boundary by an asymptotically stable random walk. Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 3, pp. 459-481. http://geodesic.mathdoc.fr/item/TVP_2015_60_3_a2/

[1] Afanasyev V. I., Geiger J., Kersting G., Vatutin V. A., “Criticality for branching processes in random environment”, Ann. Probab., 33:2 (2005), 645–673 | DOI | MR | Zbl

[2] Aurzada F., Kramm T., The first passage time problem over a moving boundary for asymptotically stable Lévy processes, arXiv: 1305.1203

[3] Aurzada F., Kramm T., Savov M., First passage times of Lévy processes over a one-sided moving boundary, arXiv: 1201.1118 | MR

[4] Denisov D., Wachtel V., “Random walks in cones”, Ann. Probab., 43:3 (2015), 992–1044, arXiv: 1110.1254 | DOI | MR | Zbl

[5] Doney R. A., “Local behaviour of first passage probabilities”, Probab. Theory Relat. Fields, 152:3–4 (2012), 559–588 | DOI | MR | Zbl

[6] Erickson K. B., “The strong law of large numbers when the mean is undefined”, Trans. Amer. Math. Soc., 185 (1973), 371–381 | DOI | MR

[7] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, t. 2, Mir, M., 1984, 752 pp. | MR

[8] Greenwood P. E., Monroe I., “Random stopping preserves regular variation of process distributions”, Ann. Probab., 5:1 (1977), 42–51 | DOI | MR | Zbl

[9] Greenwood P. E., Novikov A. A., “One-sided boundary crossing for processes with independent increments”, Teoriya veroyatn. i ee primen., 31:2 (1986), 221–232 | MR

[10] Hambly B. M., Kersting G., Kyprianou A. E., “Law of the iterated logarithm for oscillating random walks conditioned to stay non-negative”, Stochastic Process. Appl., 108:2 (2003), 327–343 | DOI | MR | Zbl

[11] Mogulskii A.A. Pecherskii E.A., “O vremeni pervogo popadaniya v oblast s krivolineinoi granitsei”, Sib. matem. zhurn., 19:4 (1978), 824–841 | MR

[12] Novikov A. A., “Martingalnyi podkhod v zadachakh o vremeni pervogo peresecheniya nelineinykh granits”, Tr. MIAN, 158 (1981), 130–152 | MR | Zbl

[13] Novikov A. A., “O vremeni peresecheniya odnostoronnei nelineinoi granitsy summami nezavisimykh velichin”, Teoriya veroyatn. i ee primen., 27:4 (1982), 643–656 | MR | Zbl

[14] Uchiyama K., “Brownian first exit from and sojourn over one-sided moving boundary and application”, Z. Wahrscheinlichkeitstheor. verw. Geb., 54 (1980), 75–116 | DOI | MR | Zbl