Branching Brownian motion in a periodic environment and existence of pulsating travelling waves

Yan-Xia Ren; Renming Song; Fan Yang

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arXiv · 2202.11253

Branching Brownian motion in a periodic environment and existence of pulsating travelling waves

Yan-Xia Ren·Renming Song·Fan Yang

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Abstract

We study the limits of the additive and derivative martingales of one-dimensional branching Brownian motion in a periodic environment. Then we prove the existence of pulsating travelling wave solutions of the corresponding F-KPP equation in the supercritical and critical cases by representing the solutions probabilistically in terms of the limits of the additive and derivative martingales. We also prove that there is no pulsating travelling wave solution in the subcritical case. Our main tools are the spine decomposition and martingale change of measures.

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Yan-Xia Ren, Renming Song, Fan Yang. 2022-02-23. Branching Brownian motion in a periodic environment and existence of pulsating travelling waves. https://arxiv.org/abs/2202.11253

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