Generalization of the Blumenthal-Getoor Index to the Class of Homogeneous Di usions with Jumps and some Applications
Loading...
Date
2012-07-04
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
We introduce the probabilistic symbol for the class of homogeneous diffusions with jumps (in
the sense of Jacod/Shiryaev). This concept generalizes the well known characteristic exponent
of a Lévy process. Using the symbol we introduce eight indices which generalize the Blumenthal-
Getoor index beta and the Pruitt index delta These indices are used afterwards to obtain growth and
Hölder conditions of the process. In the future the technical main results will be used to derive
further fine properties. Since virtually all examples of homogeneous diffusions in the literature
are Markovian, we construct a process which does not have this property.
Description
Table of contents
Keywords
COGARCH process, Feller process, fine continuity, fine properties, generalized indices, Itô process, semimartingale, symbol