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Transactions of the American Mathematical Society

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Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process


Authors: René L. Schilling and Zoran Vondraček
Journal: Trans. Amer. Math. Soc. 369 (2017), 1547-1577
MSC (2010): Primary 60J55; Secondary 60G52, 60J45, 60H10
DOI: https://doi.org/10.1090/tran/6757
Published electronically: May 2, 2016
MathSciNet review: 3581212
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Abstract: In this paper we study mutual absolute continuity and singularity of probability measures on the path space which are induced by an isotropic stable Lévy process and the purely discontinuous Girsanov transform of this process. We also look at the problem of finiteness of the relative entropy of these measures. An important tool in the paper is the question under which circumstances the a.s. finiteness of an additive functional at infinity implies the finiteness of its expected value.


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Additional Information

René L. Schilling
Affiliation: Institut für Mathematische Stochastik, Fachrichtung Mathematik, Technische Universität Dresden, 01062 Dresden, Germany
Email: rene.schilling@tu-dresden.de

Zoran Vondraček
Affiliation: Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička c. 30, 10000 Zagreb, Croatia
Email: vondra@math.hr

DOI: https://doi.org/10.1090/tran/6757
Keywords: Additive functionals, stable processes, purely discontinuous Girsanov transform, absolute continuity, singularity, relative entropy
Received by editor(s): January 31, 2015
Received by editor(s) in revised form: February 11, 2015
Published electronically: May 2, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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