The Path Operator Of Semi-dynamic Systems

In this paper,we study the correlation properties of the path operator of the semi dynamic system.The additive functional theory of Markov processes is an important part of the theory of Markov processes.The additive functional analysis of the semi dynam-ical system is the basis of the analysis of the additive functional of Piecewise-Deterministic Markov Processes.In this paper,the path operator of the semi dy-namic system is defined by the method,which can be used in any measurable function.It can obtain a class of additive functional of semi dynamical system-s.Based on the properties of the additive functional,some properties of the path operator are obtained.On the other hand,by the change of the definition,the path operator can be understood as the mapping of the measurable function to the sign of symbolic measure along the path.In this sense,some other properties of the path operator are obtained.