2018-10-11
9:00-11:00
Yifu Building 816
1.
Limit Behaviors of Stable Branching Random Walk
Mei Zhang
Beijing Normal University Email: meizhang@bnu.edu.cn
Abstract We consider a discrete-time branching random walk in the bound case, where the associated one-dimensional random walk is stable. We prove the derivative martingale Dn converges to a non trivial limit D under certain moment conditions. Moreover, we study the
1
additive martingale Wn and prove that nα Wn converges in probability, but not almost surely, to
cD∞. We also 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. The results generalize previous results in the case that the associated random walk has finite variance. This talk is based on two joint works, one is with Hui He and Jingning Liu, and another is with Jingning Liu.
2.
Large deviation principle for the maximal positions in critical branching random walks with small drifts
Hongyan Sun
School of Sciences, China University of Geosciences, Beijing Email: sun hy@cugb.edu.cn
Abstract We consider critical branching random walks V (n), n 1 on Z+. For fixed n, the displacement of an offspring from its parent is given by a nearest random walk with drift 2β/nα
towards the origin and reflected at the origin. For any κ > 2α, let M (n)
denote the right-
most position of the particles in [nκ]-th generation. We prove that, conditioned on survival to
generation [nκ], M (n)
satisfies a large deviation principle.
