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

DOI10.1214/18-ECP199zbMATH Open1409.60125arXiv1609.09338OpenAlexW2963892264MaRDI QIDQ1725484

Author name not available (Why is that?)

Publication date: 14 February 2019

Published in: (Search for Journal in Brave)

Abstract: We jointly investigate the existence of quasi-stationary distributions for one dimensional L'evy 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 L'evy processes that branches at rate $r$ and travels at velocity $c$ is equivalent to the existence of a quasi-stationary distribution for a L'evy 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 a companion article, this is not just a coincidence but the consequence of a relation between these two phenomena.

Full work available at URL: https://arxiv.org/abs/1609.09338

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Front propagation and quasi-stationary distributions for one-dimensional Lévy processes

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1725484)