On stability of traveling wave solutions for integro-differential equations related to branching Markov processes

2018/08/01 by Pasha Tkachov, Tkachov, Pasha
Mathematics · #35K57 #45K05 #47G20 #60J80 #60J85 #70K20 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:35K57 #msc:45K05 #msc:47G20 #msc:60J80 #msc:60J85 #msc:70K20

paper · pdf · doi:10.48550/arxiv.1808.00411

arxiv created 2018/08/01 · arxiv updated 2018/08/02

Abstract

The aim of this paper is to prove stability of traveling waves for integro-differential equations connected with branching Markov processes. In other words, the limiting law of the left-most particle of a (time-continuous) branching Markov process with a Lévy non-branching part is demonstrated. The key idea is to approximate the branching Markov process by a branching random walk and apply the result of Aïdékon [1] on the limiting law of the latter one.

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