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

Abstract

Let μ be a positive Kato measure on Rd associated with the Green kernel of the transient symmetric α‐stable process, the Markov process with generator (−Δ)α/2 (d>α). Let Atμ 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(Atμ).

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