An Introduction to Heavy-Tailed and Subexponential Distributions

By Serguei Foss, Dmitry Korshunov, Stan Zachary. 2011

798 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b6b631d425b84288538351d2984277f1d04005b9

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In Statistics and Probability

Citations in the corpus

Random stable looptrees (2013, neutral): “Theorem 3.6 is thus a new “one-big jump principle” (see Figure 6 for an illustration), which is a well-known phenomenon in the context of subexponential distributions (see [20] and references therein).”
Randomly weighted sums of subexponential random variables with application to capital allocation (2014, methodology): “Our study will proceed in a general setting in which the random weights θ1, . . . , θn are arbitrarily dependent and not necessarily bounded.”
Tail behavior of sums and differences of log-normal random variables (2013, background): “The log-normal distribution is an example of a subexponential distribution (see [18] for the definition of subexponentiality).”
Asymptotics of random contractions (2010, background): “Actually, for a distribution F ∈ MDA(Λ, w) with rF = ∞ and limu→∞w(u) = 0, for any λu > 0 with limu→∞ λu = 0 the function h(u) = λu/w(u) is F -insensitive in the sense of Foss et al. (2009), i.e., lim u→∞ F (u+ h(u)) F (u) = 1.”
Degree and clustering coefficient in sparse random intersection graphs (2013, neutral): “Then we have αs(m,P ) = 1√ β (Ed∗)3/2 Ed2∗ −Ed∗ + o(1).”
Branching processes with immigration in atypical random environment (2020, background): “0. Given (7), the distribution G deﬁned by its tail as G(x) = F(logx), x ≥ 1, is slowly varying at inﬁnity and therefore subexponential, that is, (8) G∗G(x) ∼ 2G(x) as x →∞, see, e.g. Theorem 3.29 in Foss et al. (2013). A distribution F with ﬁnite mean is called strong subexponential if S x 0 F(x−y)”
Tail asymptotics of supremum of certain Gaussian processes over threshold dependent random intervals (2013, background): “Following, e.g., Foss et al. (2013) we say that a non-negative random variable T is h−insensitive if P {T > u± h(u)} ∼ P {T > u} as u → ∞ for some function h(·).”