通过协调分支具有跳跃的FKPP方程的波速

IF 1.3 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2022-01-20 DOI:10.1214/23-ejp958

T. Rosati, Andr'as T'obi'as

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引用次数: 0

摘要

我们考虑由泊松随机测度驱动的具有非线性选择的Fisher KPP方程。我们证明了该方程允许由$\frac｛\mathfrak｛s｝^｛2｝｝｛2}=\int_{[0，1]｝\frac{\log｛（1+y）｝{y｝\mathfrak｛R｝（\mathrm d y）$给出的唯一波速$\mathfrak{s｝>0$，其中$\mathfrak{R｝$是驾驶噪声影响的强度。我们的论点是基于上界和下界，通过具有分支布朗运动协调系统的猝灭对偶。

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The wave speed of an FKPP equation with jumps via coordinated branching

We consider a Fisher-KPP equation with nonlinear selection driven by a Poisson random measure. We prove that the equation admits a unique wave speed $ \mathfrak{s}>0 $ given by $\frac{\mathfrak{s}^{2}}{2} = \int_{[0, 1]}\frac{ \log{(1 + y)}}{y} \mathfrak{R}( \mathrm d y)$ where $ \mathfrak{R} $ is the intensity of the impacts of the driving noise. Our arguments are based on upper and lower bounds via a quenched duality with a coordinated system of branching Brownian motions.

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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.