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 language | English (US) |
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Article number | 72 |
Journal | Electronic Journal of Probability |
Volume | 28 |
DOIs | |
State | Published - 2023 |
Keywords
- Bessel-3 process
- Brownian motion
- F-KPP equation
- branching Brownian motion
- periodic environment
- pulsating traveling waves
- spine decomposition
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty