## Electronic Journal of Probability

### Ratio of the Tail of an Infinitely Divisible Distribution on the Line to that of its Lévy Measure

#### Abstract

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.

#### Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 2, 44-74.

Dates
Accepted: 12 January 2010
First available in Project Euclid: 1 June 2016

https://projecteuclid.org/euclid.ejp/1464819787

Digital Object Identifier
doi:10.1214/EJP.v15-732

Mathematical Reviews number (MathSciNet)
MR2578382

Zentralblatt MATH identifier
1193.60023

Rights

#### Citation

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

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