117 research outputs found
Construction of -strong Feller Processes via Dirichlet Forms and Applications to Elliptic Diffusions
We provide a general construction scheme for -strong Feller
processes on locally compact separable metric spaces. Starting from a regular
Dirichlet form and specified regularity assumptions, we construct an associated
semigroup and resolvents of kernels having the -strong Feller
property. They allow us to construct a process which solves the corresponding
martingale problem for all starting points from a known set, namely the set
where the regularity assumptions hold. We apply this result to construct
elliptic diffusions having locally Lipschitz matrix coefficients and singular
drifts on general open sets with absorption at the boundary. In this
application elliptic regularity results imply the desired regularity
assumptions
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