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Feynman-Kac semigroup with discontinuous additive functionals

Authors:

Renming Song

Affiliation:

1. Department of Mathematics, Northwestern University, 60208, Evanston, Illinois

Abstract:

LetX be a symmetric stable process of index α, 0<α<2, inRd, let μ be a (signed) Radon measure onRd belonging to the Kato classKd, α and letF be a Borel function onRd×Rd satisfying certain conditions. Suppose thatA _t ^μ is the continuous additive functional with μ as its Revuz measure and

$begin{gathered} A_{t } = A_t^mu + Sigma F(X_{s - } , X_s ) hfill 0< S leqslant t hfill end{gathered}$

Keywords:	Symmetric stable processes additive functionals Revuz measure Feynman-Kac semigroup
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