Geodesic
Sudden extinction of the critical branching process in random environment
Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 3, pp. 417-438 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{TVP_2009_54_3_a0,
     author = {V. A. Vatutin and V. I. Vakhtel'},
     title = {Sudden extinction of the critical branching process in random environment},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {417--438},
     year = {2009},
     volume = {54},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a0/}
}
TY  - JOUR
AU  - V. A. Vatutin
AU  - V. I. Vakhtel'
TI  - Sudden extinction of the critical branching process in random environment
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2009
SP  - 417
EP  - 438
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a0/
LA  - ru
ID  - TVP_2009_54_3_a0
ER  - 
%0 Journal Article
%A V. A. Vatutin
%A V. I. Vakhtel'
%T Sudden extinction of the critical branching process in random environment
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2009
%P 417-438
%V 54
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a0/
%G ru
%F TVP_2009_54_3_a0
V. A. Vatutin; V. I. Vakhtel'. Sudden extinction of the critical branching process in random environment. Teoriâ veroâtnostej i ee primeneniâ, Tome 54 (2009) no. 3, pp. 417-438. http://geodesic.mathdoc.fr/item/TVP_2009_54_3_a0/

[1] Afanasyev V. I., Geiger J., Kersting G., Vatutin V. A., “Criticality for branching processes in random environment”, Ann. Probab., 33:3 (2005), 645–673 | DOI | MR | Zbl

[2] Bingham N. H., Goldie C. M., Teugels J. L., Regular Variation, Cambridge Univ. Press, Cambridge, 1987, 494 pp. | MR | Zbl

[3] Doney R., “Conditional limit theorems for asymptotically stable random walks”, Z. Warscheinlichkeitstheor. verw. Geb., 70:3 (1985), 351–360 | DOI | MR | Zbl

[4] Durrett R., “Conditioned limit theorems for some null recurrent Markov processes”, Ann. Probab., 6:5 (1978), 798–827 | DOI | MR

[5] Feller V., Vvedenie v teoriyu veroyatnostei i ee primeneniya, t. 2, Mir, M., 1984, 751 pp.

[6] Rogozin B. A., “Asimptoticheskoe povedenie koeffitsientov funktsii ot stepennykh ryadov i ryadov Fure”, Sib. matem. zhurn., 17:3 (1976), 640–648 | MR

[7] Vatutin V. A., Dyakonova E. E., “Vetvyaschiesya protsessy v sluchainoi srede: veroyatnost vyrozhdeniya v dannyi moment”, Diskretn. matem., 9:4 (1997), 100–126 | MR | Zbl

[8] Vatutin V. A., Dyakonova E. E., “Vetvyaschiesya protsessy v sluchainoi srede i butylochnye gorlyshki v evolyutsii populyatsii”, Teoriya veroyatn. i ee primen., 51:1 (2006), 22–46 | MR

[9] Vatutin V. A., Kyprianou A. E., “Branching processes in random environment die slowly”, Fifth Colloquium on Mathematics and Computer Science (September 22–26, Blaubeuren, Germany), DMTCS Proceedings Series, AG, 2008, 379–400 ; electronic: arXiv:0804.1155 | MR

[10] Vatutin V. A., Wachtel V., “Local probabilities for random walks conditioned to stay positive”, Probab. Theory Related Fields, 143:1–2 (2009), 177–217 | DOI | MR | Zbl

[11] Zolotarev V. M., “Preobrazovanie Mellina–Stiltesa v teorii veroyatnostei”, Teoriya veroyatn. i ee primen., 2:4 (1957), 445–468