跳过程的Balayage问题和可加泛函的表示

BALAYAGE PROBLEM AND REPRESENTATION OF ADDITIVE FUNCTIONALS FOR JUMP MARKOV PROCESSES

设X是一个跳过程,本文解决了X的Bahyage问题,证明了X的任何自然可加泛函均能表示为一个连续的积分型可加泛函,还建立了X的下包络原理。

Let X be a jump Markov Process. In this paper, we investigate the Balayage Problem of a new form for X which is finer than the Balayage Problem in classical case and prove a representation Theorem of additive functionals for X: If A= {A_t,t≥0} is a nature additive functional of X,then, under some conditions, there exists a non-negative function g_A such that A_t=∫_0~gA(X_)ds andthe exact form of g_A is given. Also we get the lower envelope principle: If {Ug_1,Ug_2,……} is a sequence of potential functions of X, then under certain conditions there is a non-negative function g such that inf(n≥1) Ug_=Ug.