Abstract:
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.