On the non-closure under convolution of the subexponential family

J. R. Leslie

70 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 Stochastic processes and statistical mechanics

Abstract

A distribution F of a non-negative random variable belongs to the subexponential family of distributions S if 1 – F (2)(x) ~ 2(1 – F(x)) as x →∞. This family is of considerable interest in branching processes, queueing theory, transient renewal theory and infinite divisibility theory. Much is known about the kind of distributions that belong to S but the question of whether S is closed under convolution has remained unresolved for some time. This paper contains an example which demonstrates that S is not in fact closed.

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 — 70 citations exist upstream.

References

1988Subexponential distributions and integrated tails 1980On closure and factorization properties of subexponential and related distributions 1975The Class of Subexponential Distributions 1987Convolutions of Distributions With Exponential and Subexponential Tails 1978Subexponential distributions and dominated-variation tails

Cited by

2010Ratio of the Tail of an Infinitely Divisible Distribution on the Line to that of its Lévy Measure 2015Convolution and convolution-root properties of long-tailed distributions 2011Heavy-Tailed Distributions: Data, Diagnostics, and New Developments

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.