 On the link between Markovian trees and tree-structured Markov chainsSophie Hautphenne and Benny Van Houdt European Journal of Operational Research, 2010, vol. 201, issue 3, 791-798 Abstract: In this paper, we describe a link between Markovian binary trees (MBT) and tree-like quasi-birth-and-death processes (TLQBD) by associating a specific TLQBD to each MBT. The algorithms to compute the matrices Gk in the TLQBD then correspond to the algorithms calculating the extinction probability vector of the MBT. This parallelism leads to a new quadratic algorithm, based on the Newton iteration method, which converges to the extinction probability of an MBT. We also present a one-to-one correspondence between a general Markovian tree (GMT) and a scalar tree-structured M/G/1-type Markov chain. This allows us to prove the equivalence between the main result on the positive recurrence, null recurrence or transience of a scalar tree-structured M/G/1-type Markov chain and the criticality of a GMT. Keywords: Stochastic; processes; Markovian; multi-type; branching; processes; Markovian; trees; Tree-like; quasi-birth-and-death; processes; Extinction; probability; Newton's; iteration (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:201:y:2010:i:3:p:791-798 Access Statistics for this article European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati More articles in European Journal of Operational Research from Elsevier |
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