Frontiers of Mathematics in China >
Critical survival barrier for branching random walk
Received date: 27 Aug 2018
Accepted date: 11 Dec 2019
Published date: 15 Dec 2019
Copyright
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
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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