2026-07-20T11:15:52Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:1393 2024-03-06T11:07:47Z ddc:004 open_access

Matrix Analytic Methods in Branching processes Hautphenne, Sophie Latouche, Guy Remiche, Marie-Ange Branching Processes Matrix Analytic Methods Extinction Probability Catastrophe Process We examine the question of solving the extinction probability of a particular class of continuous-time multi-type branching processes, named Markovian binary trees (MBT). The extinction probability is the minimal nonnegative solution of a fixed point equation that turns out to be quadratic, which makes its resolution particularly clear. We analyze first two linear algorithms to compute the extinction probability of an MBT, of which one is new, and, we propose a quadratic algorithm arising from Newton's iteration method for fixed-point equations. Finally, we add a catastrophe process to the initial MBT, and we analyze the resulting system. The extinction probability turns out to be much more difficult to compute; we use a $G/M/1$-type Markovian process approach to approximate this probability. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Sophie Hautphenne and Guy Latouche and Marie-Ange Remiche 2008 Is Part Of Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.07461.9 urn:nbn:de:0030-drops-13935 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.9 eng https://creativecommons.org/licenses/by/4.0/legalcode