Construction and Regularity of Transition Functions on Polish Spaces under Measurability Conditions  

作　　者：Liu-er Ye Xian-ping Guo 

机构地区：[1]College of Economics, Jinan University [2]School of Mathematics and Computational Science, Guangdong Province Key Laboratory of Computational Science, Sen-Yat Sen University

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第1期1-14,共14页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China (No.10925107);Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme;the Fundamental Research Funds for the Central Universities (No.11612314)

摘　　要：This paper concerns the construction and regularity of a transition （probability） function of a nonhomogeneous continuous-time Maxkov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous （in t ≥0） and consewative transition rates q（t, x, A）, we consider the case that q（t, x, A） axe only required to satisfy a mild measurability （in t ≥ O） condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.This paper concerns the construction and regularity of a transition （probability） function of a nonhomogeneous continuous-time Maxkov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous （in t ≥0） and consewative transition rates q（t, x, A）, we consider the case that q（t, x, A） axe only required to satisfy a mild measurability （in t ≥ O） condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.

关 键 词：Transition rate transition function construction and regularity measurability condition 

分 类 号：O174[理学—数学]