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.
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Hautphenne, S., Latouche, G. & Remiche, MA. Algorithmic Approach to the Extinction Probability of Branching Processes. Methodol Comput Appl Probab 13, 171–192 (2011). https://doi.org/10.1007/s11009-009-9141-7
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DOI: https://doi.org/10.1007/s11009-009-9141-7