纯间断马氏过程的盈函和势函的刻画及Riesz分解

纯间断马氏过程的盈函和势函的刻画及Riesz分解 RIESZ DECOMPOSTION AND CHARACTERIZATIONS OF EXCESSIVE FUNCTIONS AND POTENTIAL FUNCTIONS IN PURELY DISCONTINUOUS M ARKOV PROCESS THEORY 刘禄勤 Liu Luqin 1 first-author Department of Mathematics Wuhan University Department of Mathematics Wuhan University Department of Mathematics, Wuhan University Department of Mathematics, Wuhan University 设P（t,x,A）是抽象可测空间（E,（））中的关于q函数q（x）-q（x,A）的q过程。我们证明了:在适当的条件下,P（t,x,A）的盈函f可分解为f=h+Ug,其中h是（）函,g∈（） + 。这类似于经典的Riesz分解定理。在适当的假定下,我们还得到了非负（）-可测函数为P（t,x,A）的盈函和（）-可测函数为P（t,x,A）的势函的充要条件。 Let P（t, x, A）be a q-process in abstract measurable space （E, ） with respect to q-function q（x）-q（x, A）. The excessive function, harmonic function and potential function of p（t, x, A）are mentioned. The analog of the classical Riesz decomposition theorem is established; that is, under suitable conditions an excessive function f will be written in the form f=h+Ug where h is harmonic and g∈+. Under suitable assumptions the necessary and sufficient conditions for a nonnegative -measurable function robe an excessive function and for a nonnegative -measurable functiou to be a potential function are obtained. 马氏过程 q过程 盈函(过份函数) 纯盈函 谐函(调和函数) 势函(函数的位势) Riesz分解 Markov process q-process excessive function pure excessive funtion harmonic function potential funtion Riesz decomposition 国家自然科学基金(61672102) 1988-04-01 2021-04-01 4