The derivative martingale in a branching Lévy process

Abstract

In the study of the branching Brownian motion, the convergence of the derivative martingale is of significant interest, since the limit can be used to study the travelling wave solutions of the FKPP (Fisher–Kolmogorov–Petrovskii–Piskunov) equation.

Recently, Bertoin introduces branching Lévy processes, generalizing the branching Brownian motion to a very general class of branching particle systems. For a branching Lévy process, we obtain a necessary and sufficient condition for the convergence of the derivative martingale to a non-trivial limit. This extends previously known results for branching Brownian motions and branching random walks.

Joint work with Bastien Mallein.

Speaker

石权，中国科学院数学与系统科学研究院副研究员。2016年毕业于瑞士苏黎世大学，研究方向为Lévy过程，分支粒子系统，增长分裂过程，随机树状结构。