Q过程的μ不变测度——含吸收态情形

数学物理学报 ›› 2004, Vol. 24 ›› Issue (1): 16-25.

Q过程的μ不变测度——含吸收态情形

吴群英

桂林工学院数理系桂林 541004

出版日期:2004-02-25 发布日期:2004-02-25
基金资助:
国家自然科学基金(19871006)及广西自然科学基金资助

&mu|Invariant Measures for Q Processes——Containing an Absorbing State Case

Wu Qun-Ying

Online:2004-02-25 Published:2004-02-25
Supported by:
国家自然科学基金(19871006)及广西自然科学基金资助

摘要/Abstract

摘要：

设Q={q_{ij};i,j∈E}是可数集E上的全稳定Q矩阵, 其中E=C∪{0},C为不可约集, {0} 为吸收态，m={m_j;j∈C}是Q的有限μ不变测度, 当Q非保守和保守时, 该文分别给出存在Q过程P(t), 使m是P(t)的μ不变测度的充分必要条件, 并具体构造出Q过程P(t).

关键词: Q过程;μ次不变测度;μ不变测度;吸收态.

Abstract:

Let Q={q_{ij};i,j∈E} be a stable Q matrix over a state space E consisting of an irreducible class C and a single absorbing state 0, which is accessible from C . Suppose that Q admits a finite μ subinvariant measure m={m_j;j∈C} on C. The author considers the problem of identifying all Q processes for which m is a μ invariant measure on C.

Key words: Q processes, &mu, subinvariant measure, &mu, invariant measure, Absor bing state

中图分类号:

60J27

吴群英. Q过程的μ不变测度——含吸收态情形[J]. 数学物理学报, 2004, 24(1): 16-25.

Wu Qun-Ying. &mu|Invariant Measures for Q Processes——Containing an Absorbing State Case[J]. Acta mathematica scientia,Series A, 2004, 24(1): 16-25.