On dual generators for non-local semi-Dirichlet forms

Abstrakt

Let kx; y be a measurable function defined on E × E off the diagonal, where E is a locally compact separable metric space, and let m be a positive Radon measure on E with full support. In 2012, we showed that a quadratic form having k as a Lévy kernel becomes a lower bounded
semi-Dirichlet form on L²E;m which is non-local and regular. Then there associates a Hunt process corresponding to the semi-Dirichlet form. In the case where E = ℜ^d, we will show that the dual form of the semi-Dirichlet form also produces a Hunt process by taking a killing. As a byproduct, a precise description of the infinitesimal generator of the dual form is also given.