On the Maximum Sequence in a Critical Branching Process
Athreya, K. B.
Ann. Probab., Tome 16 (1988) no. 4, p. 502-507 / Harvested from Project Euclid
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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].
Publié le : 1988-04-14
Classification:  Branching process,  critical,  maximum,  60J80,  60K99 
@article{1176991770,
     author = {Athreya, K. B.},
     title = {On the Maximum Sequence in a Critical Branching Process},
     journal = {Ann. Probab.},
     volume = {16},
     number = {4},
     year = {1988},
     pages = { 502-507},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176991770}
}

Athreya, K. B. On the Maximum Sequence in a Critical Branching Process. Ann. Probab., Tome 16 (1988) no. 4, pp.  502-507. http://gdmltest.u-ga.fr/item/1176991770/