Open Access
2023 The wave speed of an FKPP equation with jumps via coordinated branching
Tommaso Rosati, András Tóbiás
Author Affiliations +
Electron. J. Probab. 28: 1-29 (2023). DOI: 10.1214/23-EJP958


We consider a Fisher–KPP equation with nonlinear selection driven by a Poisson random measure. We prove that the equation admits a unique wave speed s>0 given by


where R is the intensity of the impacts of the driving noise. Our arguments are based on upper and lower bounds via a quenched duality with a coordinated system of branching Brownian motions.

Funding Statement

TR gratefully acknowledges financial support through the Royal Society grant RP\R1\191065. This research was partially supported by the ERC Consolidator Grant 772466 “NOISE”.


We thank J. Blath, M. Hammer, N. Hansen, F. Hermann, A. González Casanova, N. Kurt, B. Mallein, F. Nie and M. Wilke Berenguer for interesting discussions and comments. We also thank two anonymous reviewers for insightful suggestions and corrections.


Download Citation

Tommaso Rosati. András Tóbiás. "The wave speed of an FKPP equation with jumps via coordinated branching." Electron. J. Probab. 28 1 - 29, 2023.


Received: 20 January 2022; Accepted: 12 May 2023; Published: 2023
First available in Project Euclid: 2 June 2023

Digital Object Identifier: 10.1214/23-EJP958

Primary: coordinated branching , Fisher-KPP , moment duality , wave speed

Keywords: 35C07 , 60H15 , 60J80 , 92D25

Vol.28 • 2023
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