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

2024/06/27 by Fritsch, Coralie, Villemonais, Denis, Zalduendo, Nicolás
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2406.19559

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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