Algorithmic Approach to the Extinction Probability of Branching Processes

Sophie Hautphenne (), Guy Latouche and Marie-Ange Remiche
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Sophie Hautphenne: Université Libre de Bruxelles
Guy Latouche: Université Libre de Bruxelles
Marie-Ange Remiche: Université Libre de Bruxelles

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 1, 171-192

Abstract: Abstract The extinction probability of a branching process is characterized as the solution of a fixed-point equation which, for a fairly general class of Markovian branching processes, is vector quadratic. We address the question of solving that equation, using a mixture of algorithmic and probabilistic arguments. We compare the relative efficiency of three iterative methods based on functional iteration, on the basis of the probabilistic interpretation of the successive iterations as well as on the basis of traditional rate of convergence analysis. We illustrate our findings through a few numerical examples and conclude by showing how they extend to more complex systems.

Keywords: Branching processes; Matrix analytic methods; Extinction probability; 60J80; 60J22; 92D25; 65H10 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-009-9141-7

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