Extinction and survival of branching processes in varying environment
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| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Milano Bicocca, Via Cozzi 53, I-20125 Milan - Italy
[2] Univ Sao Paulo, Ave Trabalhador Sao Carlense 400, BR-13560590 Sao Carlos, SP - Brazil
[3] Politecn Milan, Dipartimento Matemat, Piazza Leonardo da Vinci 32, I-20133 Milan - Italy
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS; v. 34, n. 3, p. 613-628, AUG 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
This paper deals with branching processes in varying environment with selection, where the offspring distribution depends on the generation and every particle has a random fitness which can only increase along genealogical lineages (descendants with small fitness do not survive). We view the branching process in varying environment (BPVE) as a particular example of branching random walk. We obtain conditions for the survival or extinction of a BPVE (with or without selection), using fixed point techniques for branching random walks. These conditions rely only on the first and second moments of the offspring distributions. Our results can be interpreted in terms of accessibility percolation on Galton-Watson trees. In particular, we obtain that there is no accessibility percolation on almost every Galton-Watson tree where the expected number of offspring grows sublinearly in time, while superlinear growths allows percolation. This result is in agreement with what was found for deterministic trees in Nowak and Krug (Europhysics Letters 101 (2013) 66004). (AU) | |
| FAPESP's process: | 16/11648-0 - Limit theorems and phase transition results for information propagation models on graphs |
| Grantee: | Pablo Martin Rodriguez |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 15/03868-7 - Asymptotic behavior of stochastic processes on graphs and applications |
| Grantee: | Pablo Martin Rodriguez |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 17/10555-0 - Stochastic modeling of interacting systems |
| Grantee: | Fabio Prates Machado |
| Support Opportunities: | Research Projects - Thematic Grants |