Non-symmetric perturbations of symmetric Dirichlet forms.
Let \(X=(\Omega,{\mathcal F},{\mathcal F}_t,X_t,p^x)\) be a symmetric Markov diffusion process with state space \(E\) and symmetry measure \(m\). Let \(({\mathcal E},{\mathcal D})\) be the associated (strongly local, quasiregular) Dirichlet form. The authors study a class of lower order perturbation of \(({\mathcal E},{\mathcal D})\), obtaining path-space integral representations of the associated semigroups. These representations are a combination of Feynman-Kac and Girsanov formulas. To this end the authors use the Hardy class of smooth measures, which contains the Kato class of smooth measures.
scientific article; zbMATH DE number 2062733
scientific article