Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process
Probability
2015-02-11 v2
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 L\'evy 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.
Keywords
Cite
@article{arxiv.1403.7364,
title = {Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process},
author = {René L. Schilling and Zoran Vondraček},
journal= {arXiv preprint arXiv:1403.7364},
year = {2015}
}
Comments
30 pages; Lemma 3.3. and several typos corrected