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Branching Brownian motion with spatially homogeneous and point-catalytic branching

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  01 October 2019

Sergey Bocharov  and
Li Wang
Sergey Bocharov*
Affiliation:
Zhejiang University
Li Wang*
Affiliation:
Beijing University of Chemical Technology
*
*Postal address: Department of Mathematics, Zhejiang University, Zheda Road, Hangzhou 310027, China. Email address: bocharov@zju.edu.cn
**Postal address: School of Sciences, Beijing University of Chemical Technology, Beijing, China. Email address: wangli@mail.buct.edu.cn
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Abstract

We consider a model of branching Brownian motion in which the usual spatially homogeneous branching and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain time-dependent regions and as a consequence the first-order asymptotic behaviour of the rightmost particle.

Keywords

Branching Brownian motionlocal times

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60F15: Strong theorems
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 3 , September 2019 , pp. 891 - 917
Copyright
© Applied Probability Trust 2019 

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