Matthieu Jonckheere (UBA)

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 de-
veloped by S. Harris for the F-KPP equation, 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 allows to generalize the known existence conditions in both contexts.

Joint work with Pablo Groisman.
Department of Mathematics

Pontifical Catholic University of Chile (PUC-Chile)

Av. Vicuña Mackenna 4860, Macul,

Santiago – Chile

(+56 2) 2354 5779

Center for Mathematical Modeling (CMM)

Faculty of Physical and Mathematical Sciences (FCFM)

Universidad de Chile

Beauchef 851, Edificio Norte, Piso 7,

Santiago – Chile