| Infinitely dimensional control Markov branching chains in random environments |
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| 作者姓名： | HU Dihe School of Mathematics and Statistics Wuhan University Wuhan 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： | 18 January 2005 |
| 修稿时间： | 18 April 2005 |
Infinitely dimensional control Markov branching chains in random environments |
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| HU Dihe School of Mathematics and Statistics,Wuhan University,Wuhan ,China.Infinitely dimensional control Markov branching chains in random environments[J].Science in China(Mathematics),2006,49(1):27-53. |
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| Authors: | HU Dihe |
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| Institution: | 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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