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

By Toshiro Watanabe, Kouji Yamamuro. 2010

69 citations recorded by the source corpus.

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 Levy 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 Levy 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.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b6f0aa006cdb8e20c1deae0a339c3c2652091a0b

Citations in the corpus

• Tempered stable distributions and processes (2013, unknown): “ν(1)(dx) := 1 ν((1,∞)) 1(1,∞)(x)ν(dx) According to [38] we say that ν(1) ∈ L(γ) for some γ ≥ 0, if for all a ∈ R we have ν(1)(r + a) ∼ eν(1)(r) as r →∞.”