单生（死）Q矩阵零流出（入）的判别准则

王玲娣, 张余辉

数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 681-692.

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数学学报 ›› 2014, Vol. 57 ›› Issue (4) : 681-692. DOI: 10.12386/A2014sxxb0063
论文

单生（死）Q矩阵零流出（入）的判别准则

    王玲娣1, 张余辉2
作者信息 +

Criteria for Zero-Exit (-Entrance) of Single-Birth (-Death) Q-Matrices

    Ling Di WANG1, Yu Hui ZHANG2
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文章历史 +

摘要

分析的方法分别给出了单生Q矩阵零流出和单死Q矩阵零流入的判别准则，统一处理了保守和非保守两种情形，再次得到了非保守的生灭Q矩阵零流出和零流入的判别准则. 同时，还类比处理了保守和非保守两种情形下带移民的单生Q矩阵的相应问题.

Abstract

In the paper, the explicit criteria for zero-exit (resp., zero-entrance) of (possible non-conservative) single birth (resp., single death) Q-matrices are presented with an analytic proof and a unified treatment is given for the conservative and non-conservative cases. Moreover, the criteria for zero-exit and zero-entrance of nonconservative birth-death Q-matrices are obtained again. Meanwhile, a similar treatment is given for the corresponding problem of single birth Q-matrices with immigration.

关键词

单生过程 / 单死过程 / 流出解 / 流入解

Key words

single birth processes / single death processes / exit-solution / entrancesolution

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王玲娣, 张余辉. 单生（死）Q矩阵零流出（入）的判别准则. 数学学报, 2014, 57(4): 681-692 https://doi.org/10.12386/A2014sxxb0063
Ling Di WANG, Yu Hui ZHANG. Criteria for Zero-Exit (-Entrance) of Single-Birth (-Death) Q-Matrices. Acta Mathematica Sinica, Chinese Series, 2014, 57(4): 681-692 https://doi.org/10.12386/A2014sxxb0063

参考文献

[1] Anderson W. J., Continuous-Time Markov Chains, Springer-Verlag, New York, 1991.

[2] Chen A. Y., Pollett P., Zhang H. J., et al., Uniqueness criteria for continuous-time Markov chains with general transition structure, Adv. Appl. Probab., 2005, 37(4): 1056-1074.

[3] Chen A. Y., Renshaw E., Existence and Uniqueness criterion for conservative uni-instantaneous denumerable Markov processes, Probab. Theory Related Fields, 1993, 94: 427-456.

[4] Chen A. Y., Renshaw E., Markov branching process with instantaneous immigration, Probab. Theory Related Fields, 1990, 87: 204-240.

[5] Chen M. F., From Markov Chains to Non-Equilibrium Particle Systems, World Scientific, Singapore, 2004.

[6] Chen M. F., Single birth processes, Chinese Ann. Math., 1999, 20B: 77-82.

[7] Hart A. G., Pollett P. K., Direct Analytical Methods for Determining Quasistationary Distributions for Continuous-time Markov Chains, In Athens Conference on Applied Probability and Time Series Analysis (Lecture Notes Statist 114), eds. Heyde C. C. et al., Springer, New York, 1996, 1: 116-126.

[8] Hart A. G., Pollett P. K., New methods for determining quasistationary distributions for Markov chains, Math. Computer Modeling, 2000, 31: 143-150.

[9] Hou Z. T., Guo Q. F., Homogeneous Denumerable Markov Process, Springer, Berlin, 1988.

[10] Reuter G. E. H., Denumerable Markov processes and the associtaed construction semigroup on l, Acta Math., 1976, 97: 1-46.

[11] Yan S. J., Chen M. F., Multidimensional Q-processes, Chinese Ann. Math., 1986, 7B: 90-110.

[12] Zhang J. K., On the generalized birth and death processes (I), Acta Math. Sci., 1984, 4: 241-259.

[13] Zhang Y. H., Birth-death-catastrophe type single birth Q-matrices (in Chinese), J. Beijing Normal Univ., 2011, 47(4): 347-350.

[14] Zhang Y. H., Zhao Q. Q., Single birth processes with immigration, Acta Mathematica Sinica, Chinese Series, 2010, 53(5): 833-846.

基金

国家自然科学基金资助项目（11131003）；国家教育部“985”计划和高校博士点专项研究基金资助项目（20100003110005）；中央高校基本科研业务费专向资金资助项目

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