Bivariate Revuz measures and the Feynman-Kac formula

In the first part of the present paper additive and multiplicative functionals of a right Markov process are investigated systematically in the setting of weak duality, by means of bivariate Revuz measures. We first give a representation for such measures. It is proved that additive and multiplicative functionals are uniquely determined by their bivariate Revuz measures and two multiplicative functionals are dual if and only if their bivariate Revuz measures are dual. In the second part we prove that any subprocess of a nearly symmetric Markov process is also nearly symmetric and give a generalized Feynman-Kac formula which describes the relationship between their corresponding Dirichlet forms.