具有低极大值条件下分支布朗运动的精细大偏差原理

Pub Date : 2021-02-18 DOI:10.30757/alea.v19-34

Yanjia Bai, Lisa Hartung

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引用次数: 2

摘要

摘要。将分支布朗运动调节为具有异常低的最大值会导致分支机制的抑制。在本文中，我们考虑一个分支布朗运动，条件是其最大值低于√2αt（α<1）。我们研究了在这种情况下第一次分支时间早/晚和第一次分支位置低/高的精确影响。我们通过对第一个分支的时间和位置施加额外的限制来做到这一点。我们获得了大偏差估计，以及在附加约束条件下的最佳第一分支时间和位置。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Refined Large Deviation Principle for Branching Brownian Motion Conditioned to Have a Low Maximum

A BSTRACT . Conditioning a branching Brownian motion to have an atypically low maximum leads to a suppression of the branching mechanism. In this note, we consider a branching Brownian motion conditioned to have a maximum below √ 2 α t ( α < 1). We study the precise effects of an early/late ﬁrst branching time and a low/high ﬁrst branching location under this condition. We do so by imposing additional constraints on the ﬁrst branching time and location. We obtain large deviation estimates, as well as the optimal ﬁrst branching time and location given the additional constraints.

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