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

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∈ 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）⊂L¹（E,μ） and \varepsilon_\alpha(u, v)=\int \tildev d \mu, v \in D(\varepsilon) where ~v is all ε-quasi-continuous m-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.