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Markovian trees: properties and algorithms

Author

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  • Nigel Bean
  • Nectarios Kontoleon
  • Peter 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. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • Nigel Bean & Nectarios Kontoleon & Peter Taylor, 2008. "Markovian trees: properties and algorithms," Annals of Operations Research, Springer, vol. 160(1), pages 31-50, April.
    • Handle: RePEc:spr:annopr:v:160:y:2008:i:1:p:31-50:10.1007/s10479-007-0295-9
    DOI: 10.1007/s10479-007-0295-9
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    Citations

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    Cited by:

    1. Hautphenne, Sophie & Houdt, Benny Van, 2010. "On the link between Markovian trees and tree-structured Markov chains," European Journal of Operational Research, Elsevier, vol. 201(3), pages 791-798, March.
    2. Marco Bonomelli & Rosella Giacometti & Sergio Ortobelli Lozza, 2020. "Joint tails impact in stochastic volatility portfolio selection models," Annals of Operations Research, Springer, vol. 292(2), pages 833-848, September.
    3. Sophie Hautphenne & Guy Latouche & Marie-Ange Remiche, 2011. "Algorithmic Approach to the Extinction Probability of Branching Processes," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 171-192, March.

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