Piecewise deterministic Markov processes and additive functionals of semi-dynamic systems
ZhaoYang LIU, GuoXin LIU · Scientia Sinica Mathematica · 2015
This paper is devoted to an analytic foundation for the study of general piecewise deterministic Markov processes (PDMPs, for short). It is rstly 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 are 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.