Generalised principal eigenvalues and global survival of branching Markov processes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912381064445952 |
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| author | Maillard, Pascal Tough, Oliver |
| author_facet | Maillard, Pascal Tough, Oliver |
| contents | We study necessary and sufficient criteria for global survival of discrete or continuous-time branching Markov processes. We relate these to several definitions of generalised principle eigenvalues for elliptic operators due to Berestycki and Rossi. In doing so, we extend these notions to fairly general semigroups of linear positive operators. We use this relation to prove new results about the generalised principle eigenvalues, as well as about uniqueness and non-uniqueness of stationary solutions of a generalised FKPP equation. The probabilistic approach through branching processes gives rise to relatively simple and transparent proofs under much more general assumptions, as well as constructions of (counter-)examples to certain conjectures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12127 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalised principal eigenvalues and global survival of branching Markov processes Maillard, Pascal Tough, Oliver Probability Analysis of PDEs 35B50, 35J61, 35K57, 35P15, 60J80, 60J85 We study necessary and sufficient criteria for global survival of discrete or continuous-time branching Markov processes. We relate these to several definitions of generalised principle eigenvalues for elliptic operators due to Berestycki and Rossi. In doing so, we extend these notions to fairly general semigroups of linear positive operators. We use this relation to prove new results about the generalised principle eigenvalues, as well as about uniqueness and non-uniqueness of stationary solutions of a generalised FKPP equation. The probabilistic approach through branching processes gives rise to relatively simple and transparent proofs under much more general assumptions, as well as constructions of (counter-)examples to certain conjectures. |
| title | Generalised principal eigenvalues and global survival of branching Markov processes |
| topic | Probability Analysis of PDEs 35B50, 35J61, 35K57, 35P15, 60J80, 60J85 |
| url | https://arxiv.org/abs/2505.12127 |