Front propagation and quasi-stationary distributions for one-dimensional Lévy processes
We jointly investigate the existence of quasi-stationary distributions for one dimensional Lévy processes and the existence of traveling waves for the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation associated with the same motion. Using probabilistic ideas developed by S. Harris, we show tha...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2016 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/55507 |
| Acesso em linha: | http://hdl.handle.net/11336/55507 |
| Access Level: | acceso abierto |
| Palavra-chave: | QUASI-STATIONARY MEASURES TRAVELLING WAVES BRANCHING LÉVY PROCESSES https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | We jointly investigate the existence of quasi-stationary distributions for one dimensional Lévy processes and the existence of traveling waves for the Fisher-Kolmogorov-Petrovskii-Piskunov (F-KPP) equation associated with the same motion. Using probabilistic ideas developed by S. Harris, we show that the existence of a traveling wave for the F-KPP equation associated with a centered Lévy processes that branches at rate r and travels at velocity c is equivalent to the existence of a quasi-stationary distribution for a Lévy process with the same movement but drifted by −c and killed at zero, with mean absorption time 1/r. This also extends the known existence conditions in both contexts. As it is discussed in [12], this is not just a coincidence but the consequence of a relation between these two phenomena. |
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