Ratio of The Tail of An Infinitely Divisible Distribution on The Line to That of Its Lévy Measure∗
نویسندگان
چکیده
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 μ(r) of an infinitely divisible distribution μ to the right tail ν(r) of its Lévy measure ν as r →∞ are estimated from above and below by reviving Teugels’s classical method. The exponential class and the dominated varying class are studied in detail.
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