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
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.
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