Maximum of the Critical Galton--Watson Processes and Left-Continuous Random Walks

Maximum of the Critical Galton--Watson Processes and Left-Continuous Random Walks Full article

Journal

Theory of Probability and its Applications
ISSN: 0040-585X , E-ISSN: 1095-7219

Output data

Year: 1998, Volume: 42, Number: 1, Pages: 17–27 Pages count : 10 DOI: 10.1137/S0040585X97975903

Authors

Vatutin V.A. ¹ , Topchii V.A. ²

Affiliations

1	Steklov Mathematical Institute, Russian Academy of Sciences
2	Institute of Information Technologies and Applied Mathematics

Let Z(n), n=0,1,..., be a critical Galton--Watson branching process, Z(0)=1. Under mild conditions on the distribution of Z(1), we prove that {\bE}\max_{1\l k\l n} Z(k)\sim \log n,\quad n\rightarrow \infty.

Vatutin V.A. , Topchii V.A.
Maximum of the Critical Galton--Watson Processes and Left-Continuous Random Walks
Theory of Probability and its Applications. 1998. V.42. N1. P.17–27. DOI: 10.1137/S0040585X97975903 Scopus OpenAlex

Ватутин В.А. , Топчий В.А.
Максимум критических процессов Гальтона - Ватсона и непрерывные слева случайные блуждания
Теория вероятностей и ее применения. 1997. Т.42. №1. С.21-34. DOI: 10.4213/tvp1709 OpenAlex

≡ Scopus:	2-s2.0-0031329834
≡ OpenAlex:	W2029727678