On convolution tails

Embrechts, Paul; Goldie, Charles M.

doi:10.1016/0304-4149(82)90013-8

Cited by 220 publications

(157 citation statements)

References 13 publications

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“…For (comments on) earlier partial results in the case τ = 2, see, for example, Chover, Ney and Wainger [6,7], Cline [8], Embrechts and Goldie [10], Foss and Korshunov [15], Pakes [19], Rogozin [20], Teugels [23] and further references therein. The proof of Theorem 3 follows from Lemmas 3 and 4 in Section 7.…”

Section: Theoremmentioning

confidence: 99%

On lower limits and equivalences for distribution tails of randomly stopped sums

Denisov¹,

Foss²,

Korshunov³

2008

Bernoulli

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For a distribution F * τ of a random sum Sτ = ξ1 + • • • + ξτ of i.i.d. random variables with a common distribution F on the half-line [0, ∞), we study the limits of the ratios of tails F * τ (x)/F (x) as x → ∞ (here, τ is a counting random variable which does not depend on {ξn} n≥1 ). We also consider applications of the results obtained to random walks, compound Poisson distributions, infinitely divisible laws, and subcritical branching processes.

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Section: Theoremmentioning

confidence: 99%

On lower limits and equivalences for distribution tails of randomly stopped sums

Denisov¹,

Foss²,

Korshunov³

2008

Bernoulli

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“…(Cf. Goldie, 1982 andCline, 1983.) Suppose (1.1) holds and we write for t > s > 0 e(jz 1 Z 2 1 > t) = P(1Z I Z 2 1 > t, IZ 2 _ s)…”

Section: Sample Correlations and Regularly Varying Tall Probabilitiesmentioning

confidence: 99%

More Limit Theory for the Sample Correlation Function of Moving Averages.

Davis¹,

Resnick²

1984

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“…When α = 0, S := S (0) is the class of subexponential distributions. The subexponential or, more generally, the convolution equivalent distributions are used in modelling heavy-tailed data, such as occur in insurance applications; we refer the reader to [5], [6], [10], and the references therein for discussion and properties. Distributions in the class S (α) for α ≥ 0 are 'near to exponential' in the sense that their tails are only slightly modified exponential.…”

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confidence: 99%

Moment and MGF convergence of overshoots and undershoots for Lévy insurance risk processes

Park

Maller

2008

Adv. Appl. Probab.

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This paper is concerned with the finiteness and large-time behaviour of moments of the overshoot and undershoot of a high level, and of their moment generating functions (MGFs), for a Lévy process which drifts to −∞ almost surely. This provides information relevant to quantities associated with the ruin of an insurance risk process. Results of Klüppelberg, Kyprianou, and Maller (2004) and Doney and Kyprianou (2006) for asymptotic overshoot and undershoot distributions in the class of Lévy processes with convolution equivalent canonical measures are shown to have moment and MGF convergence extensions.

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On convolution tails

Cited by 220 publications

References 13 publications

On lower limits and equivalences for distribution tails of randomly stopped sums

On lower limits and equivalences for distribution tails of randomly stopped sums

More Limit Theory for the Sample Correlation Function of Moving Averages.

Moment and MGF convergence of overshoots and undershoots for Lévy insurance risk processes

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