On dual generators for non-local semi-Dirichlet forms

  1. Toshihiro Uemura

Abstract

Let k(x; 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 L2(E;m) which is non-local and regular. Then there associates a Hunt process corresponding to the semi-Dirichlet form. In the case where E = ℜd, 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.

 

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Probability and Mathematical Statistics

34, z. 2, 2014

Pages from 199 to 214

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