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arXiv · 1808.00411

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

Pasha Tkachov
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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 L\'{e}vy 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 A\"{i}d\'{e}kon [1] on the limiting law of the latter one.

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Pasha Tkachov. 2018-08-01. On stability of traveling wave solutions for integro-differential equations related to branching Markov processes. https://arxiv.org/abs/1808.00411

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