周期环境中的分支布朗运动与脉动行波的存在

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2022-02-23 DOI:10.1214/23-ejp960

Y-X. Ren, R. Song, Fan Yang

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引用次数: 1

摘要

研究了周期环境下一维分支布朗运动的加性和导数鞅的极限。然后，我们证明了相应的F-KPP方程在超临界和临界情况下的脉动行波解的存在性，通过用加性和导数鞅的极限概率地表示这些解。我们还证明了在亚临界情况下不存在脉动行波解。我们的主要工具是测度的脊柱分解和鞅变换。

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

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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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.