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.
"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