On purely discontinuous additive functionals of subordinate Brownian motions

Zoran Vondraček and Vanja Wagner

Stochastic Processes and their Applications, 2018, vol. 128, issue 2, 707-725

Abstract: 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.

Keywords: Additive functionals; Subordinate Brownian motion; Purely discontinuous Girsanov transform; Absolute continuity; Singularity; Relative entropy (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1016/j.spa.2017.06.003

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