Geodesic
Maximum of the critical Galton–Watson processes and left-continuous random walks
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 21-34 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $Z(n)$, $n=0,1,\dots$ be a critical Galton–Watson branching process, $Z(0)=1$. Under mild conditions on the distribution of $Z(1)$, we prove that $$ \mathsf{E}\max_{1\le k\le n}Z(k)\sim\log n, \qquad n\to\infty. $$
Keywords: critical branching process, maximum of a branching process, the von Bahr–Esseen inequality, left-continuous random walk. 
@article{TVP_1997_42_1_a1,
     author = {V. A. Vatutin and V. A. Topchii},
     title = {Maximum of the critical {Galton{\textendash}Watson} processes and left-continuous random walks},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {21--34},
     year = {1997},
     volume = {42},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a1/}
}
TY  - JOUR
AU  - V. A. Vatutin
AU  - V. A. Topchii
TI  - Maximum of the critical Galton–Watson processes and left-continuous random walks
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1997
SP  - 21
EP  - 34
VL  - 42
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a1/
LA  - ru
ID  - TVP_1997_42_1_a1
ER  - 
%0 Journal Article
%A V. A. Vatutin
%A V. A. Topchii
%T Maximum of the critical Galton–Watson processes and left-continuous random walks
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1997
%P 21-34
%V 42
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a1/
%G ru
%F TVP_1997_42_1_a1
V. A. Vatutin; V. A. Topchii. Maximum of the critical Galton–Watson processes and left-continuous random walks. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 1, pp. 21-34. http://geodesic.mathdoc.fr/item/TVP_1997_42_1_a1/