ABSOLUTE CONTINUITY AND SINGULARITY OF PROBABILITY MEASURES INDUCED BY A PURELY DISCONTINUOUS GIRSANOV TRANSFORM OF A STABLE PROCESS

作者：Schilling Rene L^*; Vondracek Zoran

来源：Transactions of the American Mathematical Society, 2017, 369(3): 1547-1577.

DOI：10.1090/tran/6757

• Additive functionals
• stable processes
• purely discontinuous Girsanov transform
• absolute continuity
• singularity
• relative entropy

In this paper we study mutual absolute continuity and singularity of probability measures on the path space which are induced by an isotropic stable Levy 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.

• 出版日期2017-3