Markovian trees: properties and algorithms

Markovian trees: properties and algorithms

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Article ID: iaor20091345
Country: Netherlands
Volume: 160
Issue: 1
Start Page Number: 31
End Page Number: 50
Publication Date: Apr 2008
Journal: Annals of Operations Research
Authors: , ,
Keywords: Matrix-analytic methods
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.

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