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June 2006 On Lα-convergence (1≤α≤2) for a bisexual branching process with population-size dependent mating
Manuel Molina, Manuel Mota, Alfonso Ramos
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Bernoulli 12(3): 457-468 (June 2006). DOI: 10.3150/bj/1151525130

Abstract

We investigate the Lα-convergence, 1≤α≤2, of the class of bisexual branching processes with population-size dependent mating, suitably normalized, to a finite limit W such that P(W>0)>0. Through different probabilistic approaches, we provide some necessary and sufficient conditions for such convergence. In particular we establish, by analogy with the classical Kesten and Stigum result for Bienaymé-Galton-Watson processes, a logarithmic criterion for L1-convergence.

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Manuel Molina. Manuel Mota. Alfonso Ramos. "On Lα-convergence (1≤α≤2) for a bisexual branching process with population-size dependent mating." Bernoulli 12 (3) 457 - 468, June 2006. https://doi.org/10.3150/bj/1151525130

Information

Published: June 2006
First available in Project Euclid: 28 June 2006

zbMATH: 1114.60067
MathSciNet: MR2232726
Digital Object Identifier: 10.3150/bj/1151525130

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

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Vol.12 • No. 3 • June 2006
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