The Annals of Probability

On the Maximum Sequence in a Critical Branching Process

K. B. Athreya

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60K99: None of the above, but in this section

Keywords
Branching process critical maximum

Citation

Athreya, K. B. On the Maximum Sequence in a Critical Branching Process. Ann. Probab. 16 (1988), no. 2, 502--507. doi:10.1214/aop/1176991770. https://projecteuclid.org/euclid.aop/1176991770


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