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Abraham, Romain; Delmas, Jean-François

A continuum-tree-valued Markov process. (English) Zbl 1252.60072

Ann. Probab. 40, No. 3, 1167-1211 (2012).
The authors present a construction of a Lévy continuum random tree (CRT) associated with a super-critical continuous state branching process by means of the exploration process and a Girsanov theorem. They also extend the pruning procedure to this super-critical case.
Reviewer: Arnaud Durand (Paris)

Cited in 6 Reviews
Cited in 23 Documents

MSC:

60J25 Continuous-time Markov processes on general state spaces
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

continuum random tree; explosion time; pruning; tree-valued Markov process; continuous state branching process; exploration process
PDFBibTeX XMLCite
\textit{R. Abraham} and \textit{J.-F. Delmas}, Ann. Probab. 40, No. 3, 1167--1211 (2012; Zbl 1252.60072)
Full Text: DOI arXiv Euclid

References:

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