Quasi-limiting behaviour of the sub-critical Multitype Bisexual Galton-Watson Branching Process

Coralie Fritsch; Denis Villemonais; Nicolás Zalduendo

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arXiv · 2406.19559

Quasi-limiting behaviour of the sub-critical Multitype Bisexual Galton-Watson Branching Process

Coralie Fritsch·Denis Villemonais·Nicolás Zalduendo

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Abstract

We investigate the quasi-limiting behaviour of bisexual subcritical Galton-Watson branching processes. While classical subcritical Galton-Watson processes have been extensively analyzed, bisexual Galton-Watson branching processes present unique difficulties because of the lack of the branching property. To prove the existence of and convergence to one or several quasi-stationary distributions, we leverage on recent developments linking bisexual Galton-Watson branching processes extinction to the eigenvalue of a concave operator.

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Coralie Fritsch, Denis Villemonais, Nicolás Zalduendo. 2024-06-27. Quasi-limiting behaviour of the sub-critical Multitype Bisexual Galton-Watson Branching Process. https://arxiv.org/abs/2406.19559

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