Frontiers of Mathematics in China >

2019 , Vol. 14 >Issue 6: 1259 - 1280

DOI: https://doi.org/10.1007/s11464-019-0806-4

RESEARCH ARTICLE

Critical survival barrier for branching random walk

  • Jingning LIU 1 ,
  • Mei ZHANG , 2
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  • 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China
  • 2. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875, China

Received date: 27 Aug 2018

Accepted date: 11 Dec 2019

Published date: 15 Dec 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

We consider a branching random walk with an absorbing barrier, where the associated one-dimensional random walk is in the domain of attraction of an α-stable law. We shall prove that there is a barrier and a critical value such that the process dies under the critical barrier, and survives above it. This generalizes previous result in the case that the associated random walk has finite variance.

Key words： Branching random walk; α-stable spine; absorption; critical barrier

Cite this article

Jingning LIU , Mei ZHANG . Critical survival barrier for branching random walk[J]. Frontiers of Mathematics in China, 2019 , 14(6) : 1259 -1280 . DOI: 10.1007/s11464-019-0806-4

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