跳过程的Balayage问题和可加泛函的表示

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 刘禄勤 Liu Luqin 1 2 first-author 武汉大学数学系,武汉 武汉大学数学系,武汉 Department of Mathematics,Wuhan University Department of Mathematics,Wuhan University ,430072 ,430072 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 g A（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. 位势 跳过程 可加泛函 Balayage问题 下包络原理 potential jump process additive functional Balayage problem envelope principle O211.62 国家自然科学基金资助的课题;国家教委“留学回国人员科研资助费”资助的课题 1993-03-01 2021-04-01 3