Generalized Kac's moment formula for positive continuous additive functionals of Markov processes

Abstract

We establish a formula for moments of certain random variables involving positive continuous additive functionals (PCAFs) of standard processes which have absolutely continuous transition functions and are in duality with standard processes with absolutely continuous transition functions,generalizing the classical Kac's moment formula. In particular, all our results are applicable to the more familiar case of symmetric Hunt processes which are associated with regular Dirichlet forms and have absolutely continuous transition functions.