Electronic Journal of Probability

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

Toshiro Watanabe and Kouji Yamamuro

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E07: Infinitely divisible distributions; stable distributions
Secondary: 60F99: None of the above, but in this section

infinite divisibility L'evy measure $O$-subexponentiality dominated variation exponential class

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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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