逐段决定Markov过程与半动力系统可加泛函

Piecewise deterministic Markov processes and additive functionals of semi-dynamic systems

本文致力于奠定一般逐段决定Markov过程理论的新的分析基础.本文首次引入半动力系统可加泛函的概念,系统地分析它的性质,特别是得到半动力系统可加泛函对半动力系统轨道的本质依赖特征,给出它的Lebesgue分解式.半动力系统可加泛函这一概念与逐段决定Markov过程的条件跳时分布和过程的可加泛函等都有着本质的联系.

This paper is devoted to an analytic foundation for the study of general piecewise deterministic Markov processes （PDMPs, for short）. It is firstly introduced the concept of the additive functionals of a semi- dynamic system in this paper. Furthermore, a systematic study of the additive functionals is presented. It is pointed out that the additive functionals ave intrinsically dependent on the trajectories of the semi-dynamic system. This concept is closely related with the conditional distributions of the jumping times of a PDMP, the additive functionals of the process, etc.