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Type: Journal article
Title: Markovian trees: properties and algorithms
Author: Bean, N.
Kontoleon, N.
Taylor, P.
Citation: Annals of Operations Research, 2008; 160(1):31-50
Publisher: Kluwer Academic Publishers
Issue Date: 2008
ISSN: 0254-5330
Statement of
Nigel G. Bean, Nectarios Kontoleon and Peter G. Taylor
Abstract: In this paper we introduce a structure called the Markovian tree (MT). We define the MT and explore its alternative representation as a continuous-time Markovian Multitype Branching Process. We then develop two algorithms, the Depth and Order algorithms to determine the probability of eventual extinction of the MT process. We show that both of these algorithms have very natural physically intuitive interpretations and are analogues of the Neuts and U algorithms in Matrix-analytic Methods. Furthermore, we show that a special case of the Depth algorithm sheds new light on the interpretation of the sample paths of the Neuts algorithm.
Keywords: Branching processes; Matrix analytic methods
Description: The original publication can be found at
Provenance: Published online: 6 December 2007
RMID: 0020074275
DOI: 10.1007/s10479-007-0295-9
Appears in Collections:Mathematical Sciences publications
Environment Institute publications

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