Girsanov transformation for non-symmetric Markov processes

Abstract

In this paper, we study the transformation of an arbitrary non-symmetric Markov process $X$ by multiplicative functionals which are the exponential of continuous additive functionals of $X$ with zero quadratic variations. We characterize the transformed semigroups by their associated quadratic forms. For a pair of dual Markov process $(X,\hat{X})$ associated with a non-symmetric Dirichlet form, we give a necessary and sufficient condition for the Girsanov transformed processes of $X$ and $\hat{X}$ to be dual with respect to another reference measure.