par Hautphenne, Sophie 
;Latouche, Guy ;Remiche, Marie-Ange
Référence Dagstuhl seminar proceedings, 7461
Publication Publié, 2008
;Latouche, Guy ;Remiche, Marie-Ange Référence Dagstuhl seminar proceedings, 7461
Publication Publié, 2008
Article révisé par les pairs
| Résumé : | 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 diffcult to compute; we use a G/M/1-type Markovian process approach to approximate this probability. |
