Geodesic
Galton–Watson processes attaining a high level
Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 3, pp. 588-594 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Limit theorems are established for a critical Galton–Watson process attaining a high level describing the distributions of the time to attain this level and the life length of the process.
Keywords: Galton–Watson process, time to attain a level, life length, conditional invariance principles, conditional limit theorems, modified Bessel functions. 
@article{TVP_2007_52_3_a8,
     author = {V. I. Afanasyev},
     title = {Galton{\textendash}Watson processes attaining a high level},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {588--594},
     year = {2007},
     volume = {52},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2007_52_3_a8/}
}
TY  - JOUR
AU  - V. I. Afanasyev
TI  - Galton–Watson processes attaining a high level
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2007
SP  - 588
EP  - 594
VL  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TVP_2007_52_3_a8/
LA  - ru
ID  - TVP_2007_52_3_a8
ER  - 
%0 Journal Article
%A V. I. Afanasyev
%T Galton–Watson processes attaining a high level
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2007
%P 588-594
%V 52
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_2007_52_3_a8/
%G ru
%F TVP_2007_52_3_a8
V. I. Afanasyev. Galton–Watson processes attaining a high level. Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 3, pp. 588-594. http://geodesic.mathdoc.fr/item/TVP_2007_52_3_a8/

[1] Lindvall T., “On the maximum of a branching process”, Scand. J. Statist., 3:4 (1976), 209–214. | MR | Zbl

[2] Borovkov K. A., Vatutin V. A., “On distribution tails and expectations of maxima in critical branching processes”, J. Appl. Probab., 33:3 (1996), 614–622 | DOI | MR | Zbl

[3] Durrett R. T., “Conditioned limit theorems for some null recurrent Markov processes”, Ann. Probab., 6:5 (1978), 798–828 | DOI | MR | Zbl

[4] Lindvall T., “Convergence of critical Galton–Watson branching processes”, J. Appl. Probab., 9 (1972), 445–450 | DOI | MR | Zbl

[5] Lindvall T., “Limit theorems for some functionals of certain Galton–Watson branching processes”, Adv. Appl. Probab., 6 (1974), 309–321 | DOI | MR | Zbl

[6] Pakes A. G., “A limit theorem for the maxima of the para-critical simple branching process”, Adv. Appl. Probab., 30:3 (1998), 740–756 | DOI | MR | Zbl

[7] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, Nauka, M., 1981, 798 pp. | MR | Zbl