The wave speed of an FKPP equation with jumps via coordinated branching

2022/01/20 by Tommaso Rosati, Rosati, Tommaso, András Tóbiás +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #35C07 #60H15 #60J80 #92D25 #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2201.08196

openalex publication_date 2022/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \mathfraks> 0 given by \frac\mathfraks²2 = ∫_{[0, 1]}\frac log(1 + y)y \mathfrakR( \mathrm d y) where \mathfrakR 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.

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