Large time asymptotics of Feynman-Kac functionals for symmetric stable processes

Let be a positive Kato measure on Rd associated with the Green kernel of the transient symmetric -stable process, the Markov process with generator (-)/2 (d>). Let be the positive continuous additive functional in the Revuz correspondence with . If, in addition, is of compact support, we give exact large time asymptotics of the expectation of the Feynman-Kac functional, exp(A(t)(mu)).