We show that a large class of regular symmetric Dirichlet forms is generated by pseudo differential operators. We calculate the symbols which are closely related to the semimartingale characteristics (Lévy system) of the associated stochastic processes. Using the symbol we obtain estimates for the mean sojourn time of the process for balls. These estimates and a perturbation argument enable us to prove Hölder regularity of the resolvent and semigroup; this entails that the semigroup has the Feller property.
"On the Feller property of Dirichlet forms generated by pseudo differential operators." Tohoku Math. J. (2) 59 (3) 401 - 422, 2007. https://doi.org/10.2748/tmj/1192117985