Geodesic
A double exponential law for maximal branching processes
Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 143-148

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We consider maximal branching processes defined by the recurrence relation $$ Z_{n+1}=\bigvee_{m=1}^{Z_n}\xi_{m,n}, $$ where $\vee$ stands for the operation of taking maximum, $\xi_{m,n}$, $m\ge 1$, $n\ge 0$, are independent with distribution function $F$ on $\mathbf Z_+$. We prove limit theorems for stationary distributions of the processes $\{Z^{(N)}_n\}$ with the distribution functions $F^{(N)}(x)=F^N(x)$ as $N\to\infty$ in the case where $F$ belongs to the domain of attraction of the double exponential law. This research was supported by the Russian Foundation for Basic Research, grant 00–01–00131. 
@article{DM_2002_14_3_a13,
     author = {A. V. Lebedev},
     title = {A double exponential law for maximal branching processes},
     journal = {Diskretnaya Matematika},
     pages = {143--148},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2002_14_3_a13/}
}
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A. V. Lebedev. A double exponential law for maximal branching processes. Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 143-148. http://geodesic.mathdoc.fr/item/DM_2002_14_3_a13/