Some New Results on Transition Probability  

作　　者：Yu Quan XIE 

机构地区：[1]School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第12期1965-1984,共20页数学学报（英文版）

基　　金：Hunan Provincial Natural Science Foundation of China (06JJ50004);the Construct Program of the Key Discipline in Hunan Province

摘　　要：In this paper, we study the basic properties of stationary transition probability of Markov processes on a general measurable space （E, δ）, such as the continuity, maximum probability, zero point, positive probability set,standardization, and obtain a series of important results such as Continuity Theorem, Representation Theorem, Levy Theorem and so on. These results are very useful for us to study stationary tri-point transition probability on a general measurable space （E, δ）. Our main tools such as Egoroff＇s Theorem, Vitali-Hahn-Saks＇s Theorem and the theory of atomic set and well- posedness of measure are also very interesting and fashionable.In this paper, we study the basic properties of stationary transition probability of Markov processes on a general measurable space （E, δ）, such as the continuity, maximum probability, zero point, positive probability set,standardization, and obtain a series of important results such as Continuity Theorem, Representation Theorem, Levy Theorem and so on. These results are very useful for us to study stationary tri-point transition probability on a general measurable space （E, δ）. Our main tools such as Egoroff＇s Theorem, Vitali-Hahn-Saks＇s Theorem and the theory of atomic set and well- posedness of measure are also very interesting and fashionable.

关 键 词：Markov processes stationary transition probability maximum probability uniformly standard representation theorem 

分 类 号：O211.62[理学—概率论与数理统计]