Hautphenne, Sophie ;
Latouche, Guy ;
Remiche, MarieAnge
Matrix Analytic Methods in Branching processes
Abstract
We examine the question of solving the extinction
probability of a particular class of continuoustime multitype
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
fixedpoint 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.
BibTeX  Entry
@InProceedings{hautphenne_et_al:DSP:2008:1393,
author = {Sophie Hautphenne and Guy Latouche and MarieAnge Remiche},
title = {Matrix Analytic Methods in Branching processes},
booktitle = {Numerical Methods for Structured Markov Chains},
year = {2008},
editor = {Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and MarieAnge Remiche and Peter Taylor},
number = {07461},
series = {Dagstuhl Seminar Proceedings},
ISSN = {18624405},
publisher = {Internationales Begegnungs und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1393},
annote = {Keywords: Branching Processes, Matrix Analytic Methods, Extinction Probability, Catastrophe Process}
}
2008
Keywords: 

Branching Processes, Matrix Analytic Methods, Extinction Probability, Catastrophe Process 
Seminar: 

07461  Numerical Methods for Structured Markov Chains

Related Scholarly Article: 


Issue date: 

2008 
Date of publication: 

2008 