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Contents of PMS, Vol. 34, Fasc. 2,
pages 199 - 214
 

ON DUAL GENERATORS FOR NON-LOCAL SEMI-DIRICHLET FORMS

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.

2000 AMS Mathematics Subject Classification: Primary: 31C25; Secondary: 60J75, 47G20.

Keywords and phrases: Semi-Dirichlet form, non-local operator, stable-like process.

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