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Article Dans Une Revue Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques Année : 2024

The Multi-type Bisexual Galton-Watson Branching Process

Résumé

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.
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Dates et versions

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

Identifiants

Citer

Coralie Fritsch, Denis Villemonais, Nicolás Zalduendo. The Multi-type Bisexual Galton-Watson Branching Process. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, In press. ⟨hal-03696115⟩
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