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Mathematics > Probability

arXiv:1807.11778 (math)
[Submitted on 31 Jul 2018]

Title:Maximal displacement and population growth for branching Brownian motions

Authors:Yuichi Shiozawa
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Abstract: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 Schrödinger 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.
Subjects: Probability (math.PR)
Cite as: arXiv:1807.11778 [math.PR]
  (or arXiv:1807.11778v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1807.11778
Journal reference: Illinois J. Math. 63, no. 3 (2019), 353-402
Related DOI: https://doi.org/10.1215/00192082-7854864

Submission history

From: Yuichi Shiozawa [view email]
[v1] Tue, 31 Jul 2018 12:03:25 UTC (31 KB)
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