Algorithmic approach to the extinction probability of branching processes

DOI10.1007/s11009-009-9141-7zbMath1210.60094OpenAlexW2060468169MaRDI QIDQ631488

Guy Latouche, Sophie Hautphenne, Marie-Ange Remiche

Publication date: 14 March 2011

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-009-9141-7

zbMATH Keywords

branching processesextinction probabilitymatrix analytic methods

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Numerical computation of solutions to systems of equations (65H10) Population dynamics (general) (92D25) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (14)

Extinction Probabilities of Supercritical Decomposable Branching Processes ⋮ Lyapunov exponents for branching processes in a random environment: the effect of information ⋮ A Structured Markov Chain Approach to Branching Processes ⋮ A Polynomial Time Algorithm for Computing Extinction Probabilities of Multitype Branching Processes ⋮ Matrix Structures in Queuing Models ⋮ Newton's iteration for the extinction probability of a Markovian binary tree ⋮ A modified Newton method for the quadratic vector equation arising in Markovian binary trees ⋮ On the solution of a quadratic vector equation arising in Markovian Binary Trees ⋮ The modified Newton-Shamanskii method for the solution of a quadratic vector equation arising in Markovian binary trees ⋮ Convergence of relaxed Newton method for order-convex matrix equations ⋮ Fitting Markovian binary trees using global and individual demographic data ⋮ On the link between Markovian trees and tree-structured Markov chains ⋮ Markovian Trees Subject to Catastrophes: Transient Features and Extinction Probability ⋮ Perturbation analysis of the extinction probability of a Markovian binary tree

Cites Work

• Newton's iteration for the extinction probability of a Markovian binary tree
• Markovian trees: Properties and algorithms
• Transient Markov arrival processes
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• Two servers in series, studied in terms of a Markov renewal branching process
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