ON GENERALIZED FEYNMAN-KAC TRANSFORMATION FOR MARKOV PROCESSES ASSOCIATED WITH SEMI-DIRICHLET FORMS

• Published in: Acta mathematica scientia 2016-11, Vol.36 (6), p.1683-1698
• Main Author: 韩新方 马丽
• Format: Article
• Language: English
• Subjects: 60J35; 60J55; generalized Feynman-Kac semigroup; lower semi-bounded; representation of local continuous additive functional with zero quadratic variation; semi-Dirichlet form; strong continuity; 充分条件; 半狄氏型; 广义; 形态; 微分结构; 转化; 连续可加泛函; 马尔可夫过程
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(16)30099-6

Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（ε） N L（E; m）, we have the following Pukushima＇s decomposition u（Xt）-u（X0） --- Mut ＋ Nut. Define Pu f（x） = Ex[eNT f（Xt）]. Let Qu（f,g） = ε（f,g）＋ε（u, fg） for f, g E D（ε）b. In the first part, under some assumptions we show that （Qu, D（ε）b） is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then （Put〉0is strongly continuous on L2（E;m）. If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J（E x E - d） 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf（x） = Ex[eAtf（Xt）] to be strongly continuous.