| Infinitely dimensional control Markov branching chains in random environments |
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| 引用本文： | HU Dihe School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China. Infinitely dimensional control Markov branching chains in random environments[J]. 中国科学A辑(英文版), 2006, 49(1): 27-53. DOI: 10.1007/s11425-005-0024-2 |
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| 作者姓名： | HU Dihe School of Mathematics and Statistics Wuhan University Wuhan 430072 China |
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| 作者单位： | HU Dihe School of Mathematics and Statistics，Wuhan University，Wuhan 430072，China |
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| 基金项目： | 武汉大学校科研和教改项目 |
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| 摘 要： | 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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| 关 键 词： | β-control Markov branching chain in random environment |
| 收稿时间： | 2005-01-18 |
| 修稿时间： | 2005-04-18 |
Infinitely dimensional control Markov branching chains in random environments |
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| HU Dihe. Infinitely dimensional control Markov branching chains in random environments[J]. Science in China(Mathematics), 2006, 49(1): 27-53. DOI: 10.1007/s11425-005-0024-2 |
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| Authors: | HU Dihe |
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| Affiliation: | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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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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| Keywords: | random Markov transition function generating functional extinction probability polarization and proliferation rate |
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