Random convolution of inhomogeneous distributions with \(\mathcal {O} \)-exponential tail

DOI10.15559/16-VMSTA52zbMath1349.60010arXiv1604.01620MaRDI QIDQ340814

Jonas Šiaulys, Svetlana Danilenko, Simona Paškauskaitė

Publication date: 15 November 2016

Published in: Modern Stochastics. Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.01620

zbMATH Keywords

heavy tailclosure propertyrandom sumexponential tail\(\mathcal{O} \)-exponential tailinhomogeneous distributionsrandom convolution

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Sums of independent random variables; random walks (60G50) Probability distributions: general theory (60E05) Characterization and structure theory of statistical distributions (62E10)

Related Items (6)

Closure properties of \(O\)-exponential distributions ⋮ Randomly stopped sums with consistently varying distributions ⋮ Closure property of consistently varying random variables based on precise large deviation principles ⋮ Randomly stopped maximum and maximum of sums with consistently varying distributions ⋮ Randomly stopped sums with exponential-type distributions ⋮ Randomly stopped minima and maxima with exponential-type distributions

Cites Work

• Tail asymptotics for the supremum of a random walk when the mean is not finite
• Asymptotics of randomly stopped sums in the presence of heavy tails
• On the asymptotic behaviour of Lévy processes. I: Subexponential and exponential processes
• On convolution tails
• Closure of some heavy-tailed distribution classes under random convolution
• Infinite divisibility and generalized subexponentiality
• An Introduction to Heavy-Tailed and Subexponential Distributions
• Random convolution of O-exponential distributions
• Probability and Computing
• Note on the Tail Behavior of Random Walk Maxima with Heavy Tails and Negative Drift
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