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.
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Acknowledgements
The authors are very grateful to Professor Mu-Fa Chen for his helpful comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871103, 11371061) and the Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant No. KJQN 201900514).
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Liu, J., Zhang, M. Critical survival barrier for branching random walk. Front. Math. China 14, 1259–1280 (2019). https://doi.org/10.1007/s11464-019-0806-4
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DOI: https://doi.org/10.1007/s11464-019-0806-4