Feynman-Kac semigroup with discontinuous additive functionals

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Let X be a symmetric stable process of index α, 0<α<2, in Rd, let μ be a (signed) Radon measure on Rd belonging to the Kato class Kd, α and let F be a Borel function on Rd×Rd satisfying certain conditions. Suppose that Atμ is the continuous additive functional with μ as its Revuz measure and {Mathematical expression} Then the defined semigroup {Mathematical expression} is called the Feynman-Kac semigroup. In this paper we study the Feynman-Kac semigroup (Tt)t>0 and identify the bilinear form corresponding to it.

Original languageEnglish (US)
Pages (from-to)727-762
Number of pages36
JournalJournal of Theoretical Probability
Issue number4
StatePublished - Oct 1995
Externally publishedYes


  • Feynman-Kac semigroup
  • Revuz measure
  • Symmetric stable processes
  • additive functionals

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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