On the block counting process and the fixation line of the Bolthausen-Sznitman coalescent

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Kukla, Jonas¹  Moehle, Martin¹ 

[1] Eberhard Karls Univ Tubingen, Math Inst, Morgenstelle 10, D-72076 Tubingen, Germany

关键词: Absorption time;    Block counting process;    Bolthausen Sznitman coalescent;    Fixation line;    Hitting probabilities;    Mehler semigroup;    Mittag-Leffler process;    Neveu's continuous-state branching process;    Self-decomposability;    Siegmund duality;    Spectral decomposition;   

DOI  :  10.1016/j.spa.2017.06.012

来源: Elsevier

【 摘 要 】

The block counting process and the fixation line of the Bolthausen-Sznitman coalescent are analyzed. It is shown that these processes, properly scaled, converge in the Skorohod topology to the Mittag-Leffler process and to Neveu's continuous-state branching process respectively as the initial state tends to infinity. Strong relations to Siegmund duality, Mehler semigroups and self-decomposability are pointed out. Furthermore, spectral decompositions for the generators and transition probabilities of the block counting process and the fixation line of the Bolthausen Sznitman coalescent are provided leading to explicit expressions for functionals such as hitting probabilities and absorption times. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free