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

2014/03/28 by René L. Schilling, Schilling, René L., Zoran Vondraček +1
Economics, Econometrics and Finance · Mathematics · #60G52 #60H10 #60J45 #60J55 #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories #math.PR #msc:60G52 #msc:60H10 #msc:60J45 #msc:60J55

paper · pdf · doi:10.48550/arxiv.1403.7364

30 pages; Lemma 3.3. and several typos corrected

openalex publication_date 2014/03/28 · arxiv created 2015/02/10 · arxiv updated 2015/02/11 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

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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