Markov预解式之分解与Kolmogorov Q过程之精析  

Resolvent decomposition theorems and Kolmogorov Q-process

作　　者：卢影 陈安岳 杜丽 

机构地区：[1]南方科技大学金融数学与金融工程系,深圳518055

出　　处：《中国科学：数学》2015年第5期439-460,共22页Scientia Sinica：Mathematica

摘　　要：本文应用预解算子的分解定理来研究带有限个瞬时态的Kolmogorov Q-矩阵.此模型是Kolmogorov等人早期研究的一类Q-矩阵的推广.但本文的讨论不限于存在唯一性,而是更着重于对过程性质的深刻分析.在给出一个极易验证的存在唯一性条件后,本文证明Kolmogorov Q-过程必定是常返的.一个非常好的过程遍历的充分必要条件也在本文给出.在此过程遍历的条件下,过程极限分布的简洁清晰的显式也被展示出来.过程的可逆性问题也在本文中获得了很好的完备解答.The main aim of this paper is to use the resolvent decomposition theorems to analysing the Kol- mogorov Q-process which has finitely many instantaneous states. After obtaining an elegant condition for existence and uniqueness, we focus on discussing all kinds of properties of such subtle process. In particular, we show that the Kolmogorov Q-process is always recurrent and then an easy-checking condition for positive recurrence is ob- tained. The closed form for the limiting distribution is explicitly expressed. The symmetry and reversibility of such process are also discussed and well-answered.

关 键 词：连续参数Markov链 Q-矩阵 瞬时态与稳定态 存在性 唯一性 常返性 遍历性 可逆性 

分 类 号：O211.62[理学—概率论与数理统计]