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On purely discontinuous additive functionals of subordinate Brownian motions

Author

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  • Vondraček, Zoran
  • Wagner, Vanja

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.

Suggested Citation

  • Vondraček, Zoran & Wagner, Vanja, 2018. "On purely discontinuous additive functionals of subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 707-725.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:2:p:707-725
    DOI: 10.1016/j.spa.2017.06.003
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    References listed on IDEAS

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    1. Ben-Ari, Iddo & Pinsky, Ross G., 2005. "Absolute continuity/singularity and relative entropy properties for probability measures induced by diffusions on infinite time intervals," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 179-206, February.
    2. Mimica, Ante & Vondraček, Zoran, 2014. "Unavoidable collections of balls for isotropic Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1303-1334.
    3. Kim, Panki & Song, Renming & Vondraček, Zoran, 2014. "Global uniform boundary Harnack principle with explicit decay rate and its application," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 235-267.
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