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| 引用本文： | ������. ��������е����н�����������̵ļ�����[J]. 应用概率统计, 2019, 35(1): 51-62. DOI: 10.3969/j.issn.1001-4268.2019.01.004 |
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| 作者姓名： | ������ |
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| 作者单位： | ??????????????, ???, 241003 |
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| 摘 要： |
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| 关 键 词： | ??????? ??????? ????? ????? |
Limit Theorems for Birth and Death Process with One-Side Bounded Jumps in Random Environment |
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| WANG Huaming. Limit Theorems for Birth and Death Process with One-Side Bounded Jumps in Random Environment[J]. Chinese Journal of Applied Probability and Statisties, 2019, 35(1): 51-62. DOI: 10.3969/j.issn.1001-4268.2019.01.004 |
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| Authors: | WANG Huaming |
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| Affiliation: | Department of Statistics, Anhui Normal University, Wuhu, 241003, China |
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| Abstract: | We study a birth and death process ${N_t}_{tge0}$ in i.i.d. random environment, for which at each discontinuity, one particle might be born or at most $L$ particles might be dead. Along with investigating the existence and the recurrence criterion, we also study the law of large numbers of ${N_t}$. We showthat the first passage time can be written as a functional of an $L$-type branching process in random environment and a sequence of independent and exponentially distributed random variables. Consequently, an explicit velocity of the law of large numbers can be given. |
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| Keywords: | birth and death process random environment the first passage time branching structure |
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