Quasi-limiting behaviour of the sub-critical Multitype Bisexual Galton-Watson Branching Process
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929488166649856 |
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| author | Fritsch, Coralie Villemonais, Denis Zalduendo, Nicolás |
| author_facet | Fritsch, Coralie Villemonais, Denis Zalduendo, Nicolás |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19559 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasi-limiting behaviour of the sub-critical Multitype Bisexual Galton-Watson Branching Process Fritsch, Coralie Villemonais, Denis Zalduendo, Nicolás Probability 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. |
| title | Quasi-limiting behaviour of the sub-critical Multitype Bisexual Galton-Watson Branching Process |
| topic | Probability |
| url | https://arxiv.org/abs/2406.19559 |