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 s>0 given by s2 2= ∫[0,1] log(1+y) yR(dy), 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.
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