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Infinitely dimensional control Markov branching chains in random environments

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Abstract

First of all we introduce the concepts of infinitely dimensional control Markov branching chains in random environments (β-MBCRE) and prove the existence of such chains, then we introduce the concepts of conditional generating functionals and random Markov transition functions of such chains and investigate their branching property. Base on these concepts we calculate the moments of the β-MBCRE and obtain the main results of this paper such as extinction probabilities, polarization and proliferation rate. Finally we discuss the classification of β-MBCRE according to the different standards.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Hu Dihe

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  1. Hu Dihe
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Hu, D. Infinitely dimensional control Markov branching chains in random environments. SCI CHINA SER A 49, 27–53 (2006). https://doi.org/10.1007/s11425-005-0024-2

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  • DOI: https://doi.org/10.1007/s11425-005-0024-2

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