Strong Feller Property of Sticky Reflected Distorted Brownian Motion

Martin Grothaus () and Robert Voßhall ()
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Martin Grothaus: University of Kaiserslautern
Robert Voßhall: University of Kaiserslautern

Journal of Theoretical Probability, 2018, vol. 31, issue 2, 827-852

Abstract: Abstract Using Girsanov transformations we construct from sticky reflected Brownian motion on $$[0,\infty )$$ [ 0 , ∞ ) a conservative diffusion on $$E:=[0,\infty )^n$$ E : = [ 0 , ∞ ) n , $$n \in \mathbb {N}$$ n ∈ N , and prove 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. Our studies of the mathematical model are motivated by its applications to the dynamical wetting model with $$\delta $$ δ -pinning and repulsion.

Keywords: Sticky reflected distorted Brownian motion; Strong Feller properties; Skorokhod decomposition; Wentzell boundary condition; Interface models; 60K35; 60J50; 60J55; 60J35; 82C41 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-016-0735-z

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