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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Critical Markov branching processes with general set of types

Author: H. Hering
Journal: Trans. Amer. Math. Soc. 160 (1971), 185-202
MSC: Primary 60.67
MathSciNet review: 0281272
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Abstract: This paper is concerned with the asymptotic behaviour of critical, quasi-positively regular Markov branching processes. Several results which have been established with restrictions on the set of types or on the parameter are proven on slightly different moment assumptions for an arbitrary set of types and continuous as well as discrete parameter. The methods employed are analytic and rest upon the properties of probability-generating functionals constructed from the given transition function.

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Keywords: Markov branching processes, branching transition function, discrete parameter, continuous parameter, generating functionals, generating mappings, analyticity of generating mappings, factorial moment-functionals, expansion of generating functionals, expansion in factorial moment-functionals, moment recurrence relations, moment semigroup, positively regular processes, quasi-positive regularity, critical processes, nonsingular processes, asymptotic extinction, rate of extinction, conditional distribution given nonextinction, limiting conditional distribution
Article copyright: © Copyright 1971 American Mathematical Society