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

Schilling, René; Vondraček, Zoran

doi:10.1090/tran/6757

Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process
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by René L. Schilling and Zoran Vondraček PDF

Trans. Amer. Math. Soc. 369 (2017), 1547-1577 Request permission

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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