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Spread Rate of Branching Brownian Motions

Spread Rate of Branching Brownian Motions We find the exponential growth rate of the population outside a ball with time dependent radius for a branching Brownian motion in Euclidean space. We then see that the upper bound of the particle range is determined by the principal eigenvalue of the Schrödinger type operator associated with the branching rate measure and branching mechanism. We assume that the branching rate measure is small enough at infinity, and can be singular with respect to the Lebesgue measure. We finally apply our results to several concrete models. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Spread Rate of Branching Brownian Motions

Acta Applicandae Mathematicae , Volume 155 (1) – Nov 30, 2017

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References (54)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-017-0148-8
Publisher site
See Article on Publisher Site

Abstract

We find the exponential growth rate of the population outside a ball with time dependent radius for a branching Brownian motion in Euclidean space. We then see that the upper bound of the particle range is determined by the principal eigenvalue of the Schrödinger type operator associated with the branching rate measure and branching mechanism. We assume that the branching rate measure is small enough at infinity, and can be singular with respect to the Lebesgue measure. We finally apply our results to several concrete models.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Nov 30, 2017

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