华东师范大学学报(自然科学版) ›› 2008, Vol. 2008 ›› Issue (3): 45-50.

• 数学 统计学 • 上一篇    下一篇

变化环境中Markov链状态分类的性质

黄振生   

  1. 华东师范大学, 统计与精算学系, 上海 200062
  • 收稿日期:2007-09-24 修回日期:2007-12-12 出版日期:2008-05-25 发布日期:2008-05-25
  • 通讯作者: 黄振生

Some properties of the classification of states for Markov chains in random environment(Chinese)

HUANG Zhen-sheng   

  1. Department of Statistics and Actuarial science, East China Normal University, Shanghai 200062, China
  • Received:2007-09-24 Revised:2007-12-12 Online:2008-05-25 Published:2008-05-25
  • Contact: HUANG Zhen-sheng

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摘要： 引入了绕积马氏链的特征数和状态的定义,研究了特征数L(x,0;F),和G(x,0;F)的概率性质,以此为基础,讨论了强常返和强暂留态在可达和一致可达条件下的运动的传递性，以及弱常返态的特性,从而推广了经典马氏链的相关结果.

关键词: 绕积马氏链, 强常返, 强暂留, 弱常返, 绕积马氏链, 强常返, 强暂留, 弱常返

Abstract: Some basic concepts on the states, such as strongly recurrent state, weakly recurrent state, and strongly transient state, were proposed, and the corresponding Character number L(x,0;F) and G(x,0;F) were studied. On the base of this, Criteria for the states to be accesible and uniformly accesible were given. The results generalized the corresponding results in classical Markov chains.

Key words: strongly recurrent state, strongly transient state, weakly recurrent state, skew product Markov chains, strongly recurrent state, strongly transient state, weakly recurrent state

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