## The Annals of Probability

### On the Maximum Sequence in a Critical Branching Process

K. B. Athreya

#### Abstract

If $\{Z_n\}^\infty_0$ is a critical branching process such that $E_1Z^2_1 < \infty$, then $(\log n)^{-1}E_iM_n \rightarrow i$, where $E_i$ refers to starting with $Z_0 = i$ and $M_n = \max_{0\leq j \leq n}Z_j$. This improves the earlier results of Weiner [9] and Pakes [7].

#### Article information

Source
Ann. Probab., Volume 16, Number 2 (1988), 502-507.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176991770

Digital Object Identifier
doi:10.1214/aop/1176991770

Mathematical Reviews number (MathSciNet)
MR929060

Zentralblatt MATH identifier
0643.60063

JSTOR