Abstract
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 language | English (US) |
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Pages (from-to) | 727-762 |
Number of pages | 36 |
Journal | Journal of Theoretical Probability |
Volume | 8 |
Issue number | 4 |
DOIs | |
State | Published - Oct 1995 |
Externally published | Yes |
Keywords
- Feynman-Kac semigroup
- Revuz measure
- Symmetric stable processes
- additive functionals
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty