广义生灭矩阵的对偶q-矩阵Q*及最小Q*-函数

广西师范大学学报（自然科学版） ›› 2014, Vol. 32 ›› Issue (4): 76-83.

广义生灭矩阵的对偶q-矩阵Q^及最小Q^-函数

赵海霞¹, 李扬荣², 唐生强¹

1.桂林电子科技大学数学与计算科学学院,广西桂林541004;
2.西南大学数学与统计学院,重庆400715

收稿日期:2014-02-26 发布日期:2018-09-26
通讯作者: 唐生强(1951-),男,广西桂林人,桂林电子科技大学教授。E-mail:tangsq@guet.edu.cn
基金资助:
国家自然科学基金资助项目(11071199,11361017);桂林电子科技大学创新团队项目

The Dual q-matrix Q^* and the Minimal Q^*-function of the Generalized Birth-death Matrix

ZHAO Hai-xia¹, LI Yang-rong², TANG Sheng-qiang¹

1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin Guangxi 541004, China;
2. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received:2014-02-26 Published:2018-09-26

摘要/Abstract

摘要： 本文讨论广义生灭矩阵Q的对偶q-矩阵Q^*的基本性质,结合基本性质得出在一定条件下Q^*强零入、零出的数字刻画,并由此推出在相应条件下,Q强零入当且仅当Q^*零出,Q零出当且仅当Q^*强零入,从而找到了Q与Q^*在性质上的关联。本文还讨论了最小Q^*函数的基本性质,并得出在一定条件下最小Q-函数的对偶恰是最小Q^*函数。

关键词: 广义生灭矩阵Q, 对偶q-矩阵, 小Q^*函数

Abstract: In this paper, the main properties of the dual q-matrix Q^* of the generalized birth-death matrix Q were discussed. According to these properties, the digital descriptions of Q^* is strong zero-entrance and zero-exit were found respectively. Following conclusions were got: Q is strong zero-entrance if and only if Q^* is zero-exit; Q is zero-exit if and only if Q^* is strong zero-entrance. Thus the relation between Q and Q^* were found. Besides, the main properties of the minimal Q^*-function were discussed, and the following conclusion was got, under certain conditions, the dual of the minimal Q-function is the minimal Q^*-function exactly.

Key words: generalized birth-death matrix, dual q-matrix, minimal Q^*-function

中图分类号:

O177.2

赵海霞, 李扬荣, 唐生强. 广义生灭矩阵的对偶q-矩阵Q^*及最小Q^*-函数[J]. 广西师范大学学报（自然科学版）, 2014, 32(4): 76-83.

ZHAO Hai-xia, LI Yang-rong, TANG Sheng-qiang. The Dual q-matrix Q^* and the Minimal Q^*-function of the Generalized Birth-death Matrix[J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(4): 76-83.

参考文献

[1] 王汉兴,傅云斌,颜云志,等.出生率与年龄段有关的生灭分枝树[J].中国科学:数学,2013,43(4):383-398.
[2] 夏文洁,李千目,刘凤玉,等.基于拟生灭过程的多跳Ad hoc网络洪泛方式下拥塞控制及饱和条件研究[J].计算机科学,2012,39(4):110-113.
[3] 张淑媛,卢献利.生灭过程在客服中心的应用[J].科技创新导报,2013(28):172.
[4] 赵鹏举,刘玉敏.基于生灭过程的证券市场演化模型[J].中国管理科学,2011,19(3):39-45.
[5] ANDERSON W J. Continuous-time Markov chains[M]. New York: Springer-Verlag, 1991.
[6] LI Yang-rong. Dual and Feller-Reuter-Riley transition function[J]. J Math Anal Appl,2006, 313(2):461-474.
[7] 吴群英. 广义生灭过程[M].北京: 科学出版社,2004.
[8] LI Yang-rong. Strongly monotone q-functions and a note on strong ergodicity of monotone q-functions[J]. Statisitics & Propability Letters, 2007, 77(4): 396-400.
[9] CHEN An-yue, ZHANG Han-jun. Existence, uniqueness, and constructions for stochastically monotone q-process [J]. Southeast Asian Bulletion of Math, 1999, 23(4):559-583.
[10] 谷安辉.对偶分支矩阵导出的压缩半群[J].江西师范大学学报:自然科学版,2010,34(4):404-406,425.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed