Starting with a symmetric Markov diffusion process X (with symmetry measure m and L2 (m) infinitesimal generator A) and a suitable core [Formula: see text] for the Dirichlet form of X, we describe a class of derivations defined on [Formula: see text]. Associated with each such derivation B is a drift transformation of X, obtained through Girsanov's theorem. The transformed process XB is typically non-symmetric, but we are able to show that if the "divergence" of B is positive, then m is an excessive measure for XB, and the L2 (m) infinitesimal generator of XB is an extension of f ↦ Af + B (f). The methods used are mainly probabilistic, and involve the notions of even and odd continuous additive functionals, and Nakao's stochastic divergence. These methods yield a probabilistic approach to the adjoint of the semigroup of XB, and in particular lead to a solution of a problem of W. Stannat.
On unicity of the Riesz decomposition of an excessive measure.