The Expectation Of The Functional And The Minimum Non Negative Solution Of The Markov Process With Piecewise Decision

Piecewise deterministic Markov process is a kind of widely used Markov process,and the two adjacent jump time is in accordance with the deterministic system evolution.Based on the functional characterization of the X and the A,the results of the study are as follows V1(x)(?)Ex[AT],x ? E,Expected discounted function V2(x)(?)Ex[(?)]x?E,The integral equation(in the sense of Stieltis is obtained,which is further reduced by the addition of functional,with the aid of the minimum non negative solution theo-ry,which is proved to be the minimum non negative solution of the integral equation.