Strong Feller properties and uniqueness of sticky reflected distorted Brownian motion
Martin Grothaus, Robert Voßhall · arXiv (Cornell University) · 2014
Using Girsanov transformations we construct from sticky reflected Brownian motion on $[0,\infty)$ a conservative diffusion on $E:=[0,\infty)^n$, $n \in \mathbb{N}$, and prove by the probabilistic results of [CK08] that its transition semigroup possesses the strong Feller property for a specified general class of drift functions. By identifying the Dirichlet form of the constructed process, we characterize it as sticky reflected distorted Brownian motion. In particular, the relations of the underlying analytic Dirichlet form methods to the probabilistic methods of random time changes and Girsanov transformations are presented. Moreover, we prove uniqueness of weak solutions to the corresponding stochastic differential equation and apply our results to the dynamical wetting model.