arXiv subjects

Jingning Liu

Publications and source records attributed to Jingning Liu.

3 recordsLinked to original sources

arXiv2018

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

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 $α=2$.

math.PR↗

arXiv2017

The Minimal Position of a Stable Branching Random Walk

In this paper, a branching random walk $(V(x))$ in the boundary case is studied, where the associated one dimensional random walk is in the domain of attraction of an $α-$stable law with $1<α<2$. Let $M_n$ be the minimal position of $(V(x))$ at generation $n$. We established an integral test to describe the lower limit of $M_n-\frac{1}α\log n$ and a law of iterated logarithm for the upper limit of $M_n-(1+\frac{1}α)\log n$.

math.PR↗

arXiv2016

On Seneta-Heyde Scaling for a stable branching random walk

We consider a discrete-time branching random walk in the boundary case, where the associated random walk is in the domain of attraction of an $α$-stable law with $1<α<2$. We prove that the derivative martingale $D_n$ converges to a non-trivial limit $D_\infty$ under some regular conditions. We also study the additive martingale $W_n$, and prove $n^\frac{1}αW_n$ converges in probability to a constant multiple of $D_\infty$.

math.PR↗