拟正则保正型过份函数的积分表示及h-结合过程的轨道性质

Representation of Excessive Functions and Some Path Properties of h-associated Processes of Quasi-regular Positivity Preserving Coercive Forms

本文讨论拟正则保正型α－过份函数的积分表示，证明拟正则保正型（ε，Ｄ（ε））的任意α－过份函数ｕ均可表示为εα（ｕ，ｖ）＝ｖｄμ，Ｖ Ｄ（ε）μ是 Ｅ上的σ有限测度·并证明（ε， Ｄ（ε））的ｈ－结合过程是暂留的和非保守的．

In this paper, we first give a representation of α-excessive function of quasi-regular positivity preserving coercive forms (ε, D(ε)). More precisely, for any u E D(ε), u is an α-excessive function of (ε, D(ε)) if and only if there exists a unique α-finite positive measure μ on (E, β(E)) such that μ dose not charge ε-exceptional sets, D(ε) C L1(E, μ) and where v is all ε-quasi-continuous n-version of v. Then, we prove that the h-associated processes of symmetric quasi-regular positivity preserving coercive form is transient, non-conservative and non-recurrent.