Naslov
Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process
(Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process};; ; ; ;)

Autori
Schilling L. René ; Vondraček, Zoran

Izvornik
Transactions of the American mathematical society (0002-9947) 369 (2017); 1547-1577

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Additive functionals ; stable processes ; purely discontinuous Girsanov transform ; absolute continuity ; singularity ; relative entropy

Sažetak
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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA