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

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