Electronic Journal of Probability
- Electron. J. Probab.
- Volume 15 (2010), paper no. 2, 44-74.
Ratio of the Tail of an Infinitely Divisible Distribution on the Line to that of its Lévy Measure
A necessary and sufficient condition for the tail of an infinitely divisible distribution on the real line to be estimated by the tail of its Lévy measure is found. The lower limit and the upper limit of the ratio of the right tail of an infinitely divisible distribution to the right tail of its Lévy measure are estimated from above and below by reviving Teugels's classical method. The exponential class and the dominated varying class are studied in detail.
Electron. J. Probab., Volume 15 (2010), paper no. 2, 44-74.
Accepted: 12 January 2010
First available in Project Euclid: 1 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60F99: None of the above, but in this section
This work is licensed under aCreative Commons Attribution 3.0 License.
Watanabe, Toshiro; Yamamuro, Kouji. Ratio of the Tail of an Infinitely Divisible Distribution on the Line to that of its Lévy Measure. Electron. J. Probab. 15 (2010), paper no. 2, 44--74. doi:10.1214/EJP.v15-732. https://projecteuclid.org/euclid.ejp/1464819787