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 ...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.展开更多
基金Supported by the National Natural Science Foundation of China (No.10925107)Guangdong Province Universities and Colleges Pearl River Scholar Funded Schemethe Fundamental Research Funds for the Central Universities (No.11612314)
文摘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.
