The Multi-type Bisexual Galton-Watson Branching Process - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year :

The Multi-type Bisexual Galton-Watson Branching Process


In this work we study the bisexual Galton-Watson process with a finite number of types, where females and males mate according to a "mating function" and form couples of different types. We assume that this function is superadditive, which in simple words implies that two groups of females and males will form a larger number of couples together rather than separate. In the absence of a linear reproduction operator which is the key to understand the behaviour of the model in the asexual case, we build a concave reproduction operator and use a concave Perron-Frobenius theory to ensure the existence of eigenelements. Using this tool, we find a necessary and sufficient condition for almost sure extinction as well as a law of large numbers. Finally, we study the almost sure long-time convergence of the rescaled process through the identification of a supermartingale, and we give sufficient conditions to ensure a convergence in $L^1$ to a non-degenerate limit.
Fichier principal
Vignette du fichier
Final Draft.pdf (507.68 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03696115 , version 1 (15-06-2022)



Coralie Fritsch, Denis Villemonais, Nicolás Zalduendo. The Multi-type Bisexual Galton-Watson Branching Process. 2022. ⟨hal-03696115⟩
54 View
45 Download



Gmail Facebook Twitter LinkedIn More