| Jennifer L Sinclair, Department of Mathematics, Georgia Gwinnett College |
| Title: On applications of generalized tempered stable processes |
| Abstract: This seminar introduces the class of generalized tempered stable (GTS) processes and describes the formulation of GTS processes as a natural extension of tempered stable processes, which have applications in physics and finance. GTS processes encompass variations of tempered stable processes that have been introduced in the field, including modified tempered stable processes, layered stable processes, and Lamperti stable processes. Recent variations of tempered stable processes in the literature include new applications in financial mathematics and “p-tempered distributions.” In this talk, 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. |