This work introduces the class of generalized tempered stable processes which encompass variations on tempered stable processes that have been introduced in the field, including "modified tempered stable processes", "layered stable processes", and "Lamperti stable processes". Short and long time behavior of GTS Lévy processes is characterized and the absolute continuity of GTS processes with respect to the underlying stable processes is established. Series representations of GTS Lévy processes are derived. Such representations can be used for simulation and illustration of GTS processes as well as for their theoretical study.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc90-0-10,
author = {Jan Rosi\'nski and Jennifer L. Sinclair},
title = {Generalized tempered stable processes},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {153-170},
zbl = {1210.60048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc90-0-10}
}
Jan Rosiński; Jennifer L. Sinclair. Generalized tempered stable processes. Banach Center Publications, Tome 89 (2010) pp. 153-170. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc90-0-10/