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

Yan Xia Ren, Renming Song, Fan Yang

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we first 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 traveling 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 traveling wave solution in the subcritical case. Our main tools are the spine decomposition and martingale change of measures.

Original languageEnglish (US)
Article number72
JournalElectronic Journal of Probability
Volume28
DOIs
StatePublished - 2023

Keywords

  • Bessel-3 process
  • branching Brownian motion
  • Brownian motion
  • F-KPP equation
  • periodic environment
  • pulsating traveling waves
  • spine decomposition

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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