关于转移函数的收敛性  

ON THE CONVERGENCE OF TRANSITION FUNCTIONS

作　　者：赵文强[1] 李扬荣[2] 

机构地区：[1]重庆工商大学理学院,重庆400067 [2]西南大学数学与统计学院,重庆400715

出　　处：《数学杂志》2008年第1期81-84,共4页Journal of Mathematics

基　　金：国家自然科学基金资助(19871067).

摘　　要：本文研究了参数连续Markov链中转移函数的逼近.运用算子半群方法,讨论了q-矩阵的截断矩阵对应Q-函数的收敛问题;引进q-矩阵的Yosida逼近矩阵,证明了任意Q-过程可以由一列有界Q-过程逼近.并给出了最小Q-函数收敛的q-矩阵条件.推广了相关工作.In this paper, we study the approximation of transition functions in continuous-time Markov chains by means of semigroups of linear operators. We discuss the convergence of Q-funetions of the truncated matrices of q-matrix The notion of Yosida approximation of an q-matrix is introduced, therefore we obtain that every Q-process can be approximated by a sequence of bounded Q-processes. Lastly, the condition on q-matrices in order that their minimal Q-functions convergence is presented. These results generalize and develop the recent works.

关 键 词：参数连续MARKOV链 算子半群 Q函数 Q-矩阵 逼近 

分 类 号：O177.92[理学—数学]