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Kukla, Jonas; Möhle, Martin

On the block counting process and the fixation line of the Bolthausen-Sznitman coalescent. (English) Zbl 1390.60089

Stochastic Processes Appl. 128, No. 3, 939-962 (2018).
Summary: 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.

Cited in 5 Documents

MSC:

60F05 Central limit and other weak theorems
60J27 Continuous-time Markov processes on discrete state spaces
92D15 Problems related to evolution

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
PDFBibTeX XMLCite
\textit{J. Kukla} and \textit{M. Möhle}, Stochastic Processes Appl. 128, No. 3, 939--962 (2018; Zbl 1390.60089)
Full Text: DOI arXiv

References:

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