English

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

Probability 2018-08-02 v1

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.

Keywords

Cite

@article{arxiv.1808.00411,
  title  = {On stability of traveling wave solutions for integro-differential equations related to branching Markov processes},
  author = {Pasha Tkachov},
  journal= {arXiv preprint arXiv:1808.00411},
  year   = {2018}
}