Maximal displacement and population growth for branching Brownian motions
Maximal displacement and population growth for branching Brownian motions
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DOI：
10.1215/00192082-7854864
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发表时间：
2018-07
影响因子：
0.6
通讯作者：
Yuichi Shiozawa
中科院分区：
文献类型：
--
作者：
Yuichi Shiozawa
利用Schr odinger型算子的主特征值，研究了欧氏空间中分支布朗运动的最大位移和相应的布居.我们首先确定它们在生存事件中的生长率。然后，我们建立了灭绝的可能性下的最大位移的上偏差。在非灭绝条件下，进一步讨论了临界阶段上偏差概率的衰减率和种群增长率。
We study the maximal displacement and related population for a branching Brownian motion in Euclidean space in terms of the principal eigenvalue of an associated Schr\"odinger type operator. We first determine their growth rates on the survival event. We then establish the upper deviation for the maximal displacement under the possibility of extinction. Under the non-extinction condition, we further discuss the decay rate of the upper deviation probability and the population growth at the critical phase.