Lower limits and equivalences for convolution tails

By Serguei Foss, Dmitry Korshunov. 2005

71 citations recorded by the source corpus.

Suppose F is a distribution on the half-line [0, oo). We study the limits of the ratios of tails F * F(x)/F(x) as x→ oo. We also discuss the classes of distributions &,& (y) and &*.

Subfields: Applied Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/27c857441cf337c4db479721b955b10e8ef3cb56

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Toshiro Watanabe
2. Kouji Yamamuro
3. Denis Denisov

In Finance

1. Toshiro Watanabe
2. Kouji Yamamuro
3. Denis Denisov
4. Bert Zwart
5. Serguei Foss
6. Dmitry Korshunov
7. Paweł Sztonyk
8. Mark W. Meckes

Citations in the corpus

• Asymptotics of randomly stopped sums in the presence of heavy tails (2008, background): “In particular, by considering the case τ = 2, we conclude that if F is a heavy-tailed distribution on R+ and if P{S2 > x} ∼ cF (x) asx → ∞, for some c, thenc = 2 with necessity (see [11]).”
• On a Theorem of Breiman and a Class of Random Difference Equations (2007, background): “A recent interesting paper on these classes of distributions is [9].”
• Convolution equivalence and distributions of random sums (2008, methodology): “Foss and Korshunov [ 15 ] proved a remarkable extension of Rogozin’s theorem, which was expected by [9].”
• Ratio of the Tail of an Infinitely Divisible Distribution on the Line to that of its Lévy Measure (2010, methodology): “4 Bound separating C∗ and C ∗ for μ in H The study of the lower and upper limits of ratios of tails of distributions on R+ was initiated by [11; 25] and progressed by [9; 18].”