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Multitype Branching Brownian Motion and Traveling Waves

Part of: Markov processes Representations of solutions

Published online by Cambridge University Press:  22 February 2016

Yan-Xia Ren  and
Ting Yang
Yan-Xia Ren*
Affiliation:
Peking University
Ting Yang*
Affiliation:
Chinese Academy of Sciences
*
∗ Postal address: LMAM School of Mathematical Sciences and Center for Statistical Science, Peking University, Beijing, 100871, P. R. China. Email address: yxren@math.pku.edu.cn
∗∗ Postal address: Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, P. R. China. Email address: yangt@amss.ac.cn
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Abstract

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In this article we study the parabolic system of equations which is closely related to a multitype branching Brownian motion. Particular attention is paid to the monotone traveling wave solutions of this system. Provided with some moment conditions, we show the existence, uniqueness, and asymptotic behaviors of such waves with speed greater than or equal to a critical value c̲ and nonexistence of such waves with speed smaller than c̲.

Keywords

Multitype branching Brownian motionspine approachadditive martingaletraveling wave solution

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 35C07: Traveling wave solutions
Type
Research Article
Information
Advances in Applied Probability , Volume 46 , Issue 1 , March 2014 , pp. 217 - 240
Copyright
© Applied Probability Trust 

Footnotes

Research supported in part by NNSF of China (Grant numbers 10971003, 11128101, 11271030) and Specialized Research Fund for the Doctoral Program of Higher Education.

Research supported by China Postdoctoral Science Foundation (Grant number 2013M541061).

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