Multi-type branching in varying environment

This paper considers the asymptotic theory of the varying environment Galton–Watson process with a countable set of types. This paper examines the convergence in L p and almost surely of the numbers of the various types when normalised by the corresponding expected number. The harmonic functions of...

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Bibliographic Details
Published inStochastic processes and their applications Vol. 83; no. 2; pp. 357 - 400
Main Authors Biggins, J.D., Cohn, H., Nerman, O.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.10.1999
Elsevier Science
Elsevier
SeriesStochastic Processes and their Applications
Subjects
Exact sciences and technology
Harmonic function
Harmonic function Matrix products Martingale Inhomogeneous Markov chains Lp convergence
Inhomogeneous Markov chains
Lp convergence
Markov processes
Martingale
Mathematics
Matrix products
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
Inhomogeneous Markov chains
Primary 60J80
Matrix products
L p convergence
Harmonic function
Martingale
Galton Watson process
Stochastic process
Mean estimation
Asymptotic behavior
Convergence
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Summary:This paper considers the asymptotic theory of the varying environment Galton–Watson process with a countable set of types. This paper examines the convergence in L p and almost surely of the numbers of the various types when normalised by the corresponding expected number. The harmonic functions of the mean matrices play a central role in the analysis. Many previously studied models provide particular cases.
ISSN:0304-4149
1879-209X
DOI:10.1016/S0304-4149(99)00049-6