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

Jonas Kukla and Martin Möhle

Stochastic Processes and their Applications, 2018, vol. 128, issue 3, 939-962

Abstract: 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spa.2017.06.012

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