FEYNMAN-KAC SEMIGROUP WITH DISCONTINUOUS ADDITIVE-FUNCTIONALS

Let X be a symmetric stable process of index alpha, 0 < alpha < 2, in R(d), let mu be a (signed) Radon measure on R(d) belonging to the Kato class K-d,K-alpha and let F be a Borel function on R(d) X R(d) satisf ying certain conditions. Suppose that A(t)(mu) is the continuous addit ive functional with mu as its Revuz measure and A(t) = A(t)(mu) + (0 < s less than or equal to 1)Sigma F(X(s-),X(s)) Then the defined semigr oup T(t)f(x) = E(x){e(At)f(X(t))} is called the Feynman-Kac semigroup. In this paper we study the Feynman-Kac semigroup (T-t)(t > 0) and ide ntify the bilinear form corresponding to it.