On purely discontinuous additive functionals of subordinate Brownian motions

Let At=∑s≤tF(Xs−,Xs) be a purely discontinuous additive functional of a subordinate Brownian motion X=(Xt,Px). We give a sufficient condition on the non-negative function F that guarantees that finiteness of A∞ implies finiteness of its expectation. This result is then applied to study the relative entropy of Px and the probability measure induced by a purely discontinuous Girsanov transform of the process X. We prove these results under the weak global scaling condition on the Laplace exponent of the underlying subordinator.