Critical survival barrier for branching random walk

doi:10.1007/s11464-019-0806-4

Front. Math. China

2019, Vol. 14

Issue (6) : 1259-1280 https://doi.org/10.1007/s11464-019-0806-4

RESEARCH ARTICLE

Critical survival barrier for branching random walk

Jingning LIU¹, Mei ZHANG²(

)

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

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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.

Keywords Branching random walk α-stable spine absorption critical barrier

Corresponding Author(s): Mei ZHANG

Issue Date: 07 January 2020

Cite this article:

Jingning LIU,Mei ZHANG. Critical survival barrier for branching random walk[J]. Front. Math. China, 2019, 14(6): 1259-1280.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0806-4
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I6/1259

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