  For a given quasi-regular positivity preserving coercive form, we construct a
family of ($\sigma$-finite) distribution flows associated with the semigroup of
the form. The canonical cadlag process equipped with the distribution flows
behaves like a strong Markov process. Moreover, employing distribution flows we
can construct optional measures and establish Revuz correspondence between
additive functionals and smooth measures. The results obtained in this paper
will enable us to perform a kind of stochastic analysis related to positivity
preserving coercive forms.

Probability