On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications

Jun Cai · Qihe Tang

92 citations0/0 files storedJournal of Applied Probability

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Probability and Risk Models Probability and Statistical Research Advanced Queuing Theory Analysis

Abstract

In this paper, we discuss max-sum equivalence and convolution closure of heavy-tailed distributions. We generalize the well-known max-sum equivalence and convolution closure in the class of regular variation to two larger classes of heavy-tailed distributions. As applications of these results, we study asymptotic behaviour of the tails of compound geometric convolutions, the ruin probability in the compound Poisson risk process perturbed by an α-stable Lévy motion, and the equilibrium waiting-time distribution of the M/G/k queue.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 92 citations exist upstream.

References

1997Modelling Extremal Events 1994Modelling of extremal events in insurance and finance 1982Estimates for the probability of ruin with special emphasis on the possibility of large claims 1994Subexponentiality of the product of independent random variables 1988Subexponential distributions and integrated tails 1979Subexponentiality and infinite divisibility 1991Risk theory for the compound Poisson process that is perturbed by diffusion 1980On closure and factorization properties of subexponential and related distributions

Cited by

2008Sums of Dependent Nonnegative Random Variables with Subexponential Tails 2010Approximation of the tail probability of randomly weighted sums of dependent random variables with dominated variation 2007On the time value of absolute ruin with debit interest 2007Tails of random sums of a heavy-tailed number of light-tailed terms 2004Asymptotics for the Finite Time Ruin Probability in the Renewal Model with Consistent Variation

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.