Perturbation of symmetric Markov processes

Abstract We present a path-space integral representation of the semigroup associated with the quadratic form obtained by a lower-order perturbation of the L 2 -infinitesimal generator L of a general symmetric Markov process. An illuminating concrete example for Crucial to the development is the use of an extension of Nakao's stochastic integral for zero-energy additive functionals and the associated Itô formula, both of which were recently developed i