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May 2003 Harmonic moments and large deviation rates for supercritical branching processes
P. E. Ney, A. N. Vidyashankar
Ann. Appl. Probab. 13(2): 475-489 (May 2003). DOI: 10.1214/aoap/1050689589


Let $ \{Z_{n}, n \ge 1 \}$ be a single type supercritical Galton--Watson process with mean $EZ_{1} \equiv m$, initiated by a single ancestor. This paper studies the large deviation behavior of the sequence $\{R_n \equiv \frac{Z_{n+1}}{Z_n}\dvtx n \ge 1 \}$ and establishes a "phase transition" in rates depending on whether $r$, the maximal number of moments possessed by the offspring distribution, is less than, equal to or greater than the Schröder constant $\alpha$. This is done via a careful analysis of the harmonic moments of $Z_n$.


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P. E. Ney. A. N. Vidyashankar. "Harmonic moments and large deviation rates for supercritical branching processes." Ann. Appl. Probab. 13 (2) 475 - 489, May 2003.


Published: May 2003
First available in Project Euclid: 18 April 2003

zbMATH: 1032.60081
MathSciNet: MR1970272
Digital Object Identifier: 10.1214/aoap/1050689589

Primary: 60F10 , 60J80

Keywords: branching processes , harmonic moments , large deviations

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.13 • No. 2 • May 2003
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