eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2008-04-07
1
3
10.4230/DagSemProc.07461.9
article
Matrix Analytic Methods in Branching processes
Hautphenne, Sophie
Latouche, Guy
Remiche, Marie-Ange
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.
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol07461/DagSemProc.07461.9/DagSemProc.07461.9.pdf
Branching Processes
Matrix Analytic Methods
Extinction Probability
Catastrophe Process