广生灭过程的遍历性及平稳分布

数学物理学报 ›› 1998, Vol. 18 ›› Issue (1): 25-32.

广生灭过程的遍历性及平稳分布

唐有荣, 刘再明, 侯振挺

长沙铁道学院科研所长沙 410075

收稿日期:1996-03-28 修回日期:1996-11-25 出版日期:1998-03-26 发布日期:1998-03-26
基金资助:
国家自然科学基金资助

The Ergodic Property and Equilibrium Distribution of the Generalized Birth and Death Processes

Tang Yourong, Liu Zaiming, Hou Zhenting

Research Department, Changsha Railway University, Changsha 410075

Received:1996-03-28 Revised:1996-11-25 Online:1998-03-26 Published:1998-03-26

摘要/Abstract

摘要： 文献[1]研究了广生灭过程的向上积分型随机泛函,得到了广生灭过程的若干数字特征以及常返的充要条件,该文讨论广生灭过程向下积分型随机泛函,给出了广生灭过程遍历的充要条件以及平均返回时间的计算公式,并在遍历的条件下求出了广生灭过程的平稳分布.

关键词: 随机泛函, 数字特征, 遍历性, 平稳分布

Abstract: Reference[1] has concerned upward integral random functional of the generalizedbirth and death processes and obtained several digital features of the processes and the Tish paper deals with down sary and sufficient conditions for the processes to be recurrent. This paper dcals with downward integral random functional of the generalized birth and death processes, and obtains thenecessary and sufficient conditions for the processes to be ergodic and computational formulafor average recurrent times as well as the equilibrium distributions of the processes in the ergodic conditions.

Key words: Random functional, Digital feature, Ergodic property, Equilibrium distribution

唐有荣, 刘再明, 侯振挺. 广生灭过程的遍历性及平稳分布[J]. 数学物理学报, 1998, 18(1): 25-32.

Tang Yourong, Liu Zaiming, Hou Zhenting. The Ergodic Property and Equilibrium Distribution of the Generalized Birth and Death Processes[J]. Acta mathematica scientia,Series A, 1998, 18(1): 25-32.

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