抽象空间中非时齐马氏过程的分析理论(Ⅲ)——q过程的存在性及唯一性

<正> 本文是1]、2]的续篇,一切符号及定义均沿袭1]、2]. §1.q过程的存在性 由1]定义4.1知,可微马氏过程之转移密度函数是q函数.1]文主要研究的问题是:在何种条件下,马氏过程是可微的,即有转移密度函数.而本文研究的,恰是1]之

THE ANALYTICAL THEORY OF NONHOMOGENEOUS MARKOV PROCESSES IN ABSTRACT SPACE(Ⅲ)——THE EXISTENCE AND UNIQUENESS OF Q-PROCESSES

Let be a measurable space, q(t,x,A) (t≥0, x∈, A∈) is said to be a q-function, if(ii) For fixed t≥0, x∈, q(t,x,·)is a denumerable additive set funetion on, for fixed t≥0, A∈q(t,A) is a measurable function of x.The Markov process p(s, t,x,A) is said to be a q-process, ifIn this paper, the existence and uniqueness of q-processes is investigated when q-function q(t,x,A) is a continuous function of t.