Front propagation and quasi-stationary distributions for one-dimensional Lévy processes

 

Autores
Groisman, Pablo Jose; Jonckheere, Matthieu Thimothy Samson
Tipo de recurso
artículo
Estado
Versión publicada
Año de publicación
2016
País
Argentina
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio
CONICET Digital (CONICET)
Descripción
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.
Idioma
inglés
OAI Identifier
oai:ri.conicet.gov.ar:11336/55507
Enlace del recurso
http://hdl.handle.net/11336/55507
Nivel de acceso
Acceso abierto
Materia
travelling waves
levy processes
qsd
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS