ROSIŃSKI MEASURES FOR TEMPERED STABLE AND RELATED
Wojbor A. Woyczyński
Abstract: Several concrete parametric classes of tempered stable distributions are discussed in
terms of explicit calculations of their Rosiński measures. The hope is that they will
provide a family of concrete models useful in applied areas and for which the fitting
can be done by parametric methods. Related Ornstein-Uhlenbeck processes are
analyzed. The emphasis throughout the paper is on obtaining exact analytic formulas.
2000 AMS Mathematics Subject Classification: 62M15, 60G60.
Key words and phrases: Tempered stable distributions, Ornstein-Uhlenbeck and Lévy
processes, Truncated Lévy Flights.