Generalized tempered stable processes

Volume 90 / 2010

Jan Rosiński, Jennifer L. Sinclair Banach Center Publications 90 (2010), 153-170 MSC: 60E07, 60F05, 60G51, 60G52. DOI: 10.4064/bc90-0-10

Abstract

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.

Authors

  • Jan RosińskiDepartment of Mathematics
    University of Tennessee
    1534 Cumberland Ave.
    Knoxville, TN 37996, USA
    e-mail
  • Jennifer L. SinclairSchool of Science and Technology
    Georgia Gwinnett College
    1000 University Center Lane
    Lawrenceville, GA 30043, USA
    e-mail

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