Newton's iteration for the extinction probability of a Markovian binary tree

Linear Algebra and Its Applications

Volumn 428, Issue 11-12, 2008, Pages 2791-2804

  Hautphenne, Sophie ^a   Latouche, Guy ^a   Remiche, Marie Ange ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Branching processes; Matrix analytic methods; Newton's iteration

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; MATRIX ALGEBRA; NEWTON-RAPHSON METHOD; NONLINEAR EQUATIONS; TELECOMMUNICATION SYSTEMS; CONTINUOUS TIME SYSTEMS; ITERATIVE METHODS; PROBABILITY DISTRIBUTIONS;

BRANCHING PROCESSES; FIXED POINT EQUATIONS; MATRIX ANALYTIC METHODS; NEWTON'S ITERATION;

BINARY TREES;

BRANCHING PROCESS; EXTINCTION PROBABILITY; KEYWORDS; MATRIX ANALYTIC METHODS; MINIMAL NONNEGATIVE SOLUTION; NEWTON'S ITERATION; PROBABILISTIC INTERPRETATION; SECOND-ORDER EQUATION;

EID: 41549138327     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2007.12.024     Document Type: Article

References (13)

1. Athreya K.B., and Ney P.E. Branching Processes (1972), Springer-Verlag, New York
2. N.G. Bean, N. Kontoleon, P.G. Taylor, Algorithms for determining the probability of eventual extinction of a Markovian binary tree, Technical Report, University of Adelaide & University of Melbourne, 2004.
3. Bean N.G., O'Reilly M.M., and Taylor P.G. Algorithms for return probabilities for stochastic fluid flows. Stochastic Models 21 1 (2005) 149-184
4. Haccou P., Jagers P., and Vatutin V.A. Branching Processes: Variation, Growth, and Extinction of Populations (2005), Cambridge University Press
5. Harris T.E. The Theory of Branching Processes (1963), Dover, New York
6. S. Hautphenne, G. Latouche, M.-A. Remiche, Algorithmic approach to the extinction probability of branching processes, submitted for publication.
7. Hautphenne S., Leibnitz K., and Remiche M.-A. Extinction probability in Peer-to-Peer file diffusion. ACM SIGMETRICS Perform Eval. Rev. 34 2 (2006) 3-4
8. Kimmel M., and Axelrod D.E. Branching Processes in Biology (2002), Springer-Verlag, New York
9. N. Kontoleon, The Markovian binary tree: a model of the macroevolutionary process, Ph.D. thesis, The University of Adelaide, 2005.
10. Latouche G. Newton's iteration for non-linear equations in Markov chains. J. Numer. Anal. 14 (1994) 583-598
11. Bean N., Kontoleon N., and Taylor P. Markovian trees: properties and algorithms. Ann. Oper. Res. 160 1 (2008) 31-50
12. Ortega J.M., and Rheinboldt W.C. Iterative Solution of Nonlinear Equations in Several Variables (2000), Society for Industrial and Applied Mathematics, Philadelphia, PA, USA Republication of work first published by Academic Press in 1970.
13. X. Yang, G. de Veciana, Service capacity of Peer-to-Peer networks, Technical Report, The University of Texas at Austin, 2004.