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arXiv · 1808.03407

A note on the critical barrier for the survival of $α-$stable branching random walk with absorption

Jingning Liu·Mei Zhang
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Abstract

We consider a branching random walk with an absorbing barrier, where the step of the associated one-dimensional random walk is in the domain of attraction of an $α$-stable law with $1<α<2$. We shall prove that there is a barrier $an^{\frac{1}{1+α}}$ and a critical value $a_α$ such that if $a a_α$, then the process survives. The results generalize previous results in literature for the case $α=2$.

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Jingning Liu, Mei Zhang. 2018-08-10. A note on the critical barrier for the survival of $α-$stable branching random walk with absorption. https://arxiv.org/abs/1808.03407

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