Illinois Journal of Mathematics

Maximal displacement and population growth for branching Brownian motions

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 nonextinction condition, we further discuss the decay rate of the upper deviation probability and the population growth at the critical phase.

Article information

Source
Illinois J. Math., Volume 63, Number 3 (2019), 353-402.

Dates
Received: 25 October 2018
Revised: 14 May 2019
First available in Project Euclid: 19 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1568858864

Digital Object Identifier
doi:10.1215/00192082-7854864

Mathematical Reviews number (MathSciNet)
MR4012348

Zentralblatt MATH identifier
07110746

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J65: Brownian motion [See also 58J65]

Citation

Shiozawa, Yuichi. Maximal displacement and population growth for branching Brownian motions. Illinois J. Math. 63 (2019), no. 3, 353--402. doi:10.1215/00192082-7854864. https://projecteuclid.org/euclid.ijm/1568858864


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