Heat kernel estimates and Harnack inequalities for some Dirichlet forms with non-local part.
Hitting probabilities and potential theory for the brownian path-valued process
We consider the Brownian path-valued process studied in [LG1], [LG2], which is closely related to super Brownian motion. We obtain several potential-theoretic results related to this process. In particular, we give an explicit description of the capacitary distribution of certain subsets of the path space, such as the set of paths that hit a given closed set. These capacitary distributions are characterized as the laws of solutions of certain stochastic differential equations. They solve variational...
Hitting times and spectral gap inequalities