Feynman-Kac Formula for Left Continuous Additive Functionals and Extended Kato Class Measures

The perturbation of the generator of a Borel right process by a signed measure is investigated, using probabilistic and analytic potential theoretical methods. We establish a Feynman-Kac formula associated with measures charging no polar set and belonging to an extended Kato class. A main tool of this approach is the validity of a Khas’minskii Lemma for Stieltjes exponentials of positive left continuous additive functionals.