Lower limits and upper limits for tails of random sums supported on \(\mathbb R\)

DOI10.1016/j.spl.2010.03.005zbMath1196.60027OpenAlexW2034312791MaRDI QIDQ979201

Zhaolei Cui, Yue-bao Wang, Chang Jun Yu

Publication date: 25 June 2010

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2010.03.005

zbMATH Keywords

random sumsdensityupper limitslocal distributionlower limits

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Limit theorems in probability theory (60F99)

Related Items (13)

Random walks with non-convolution equivalent increments and their applications ⋮ Some discussions on the local distribution classes ⋮ Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments ⋮ Asymptotic behavior of the ratio of tail probabilities of sum and maximum of independent random variables ⋮ Asymptotic behavior for sums of non-identically distributed random variables ⋮ Convolution and convolution-root properties of long-tailed distributions ⋮ New examples of heavy-tailed O-subexponential distributions and related closure properties ⋮ The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands ⋮ Asymptotics for the solutions to defective renewal equations ⋮ Asymptotic results for tail probabilities of sums of dependent and heavy-tailed random variables ⋮ Tail behavior of supremum of a random walk when Cramér's condition fails ⋮ The uniform local asymptotics for a Lévy process and its overshoot and undershoot ⋮ Embrechts-Goldie's problem on the class of lattice convolution equivalent distributions

Cites Work

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• Modeling teletraffic arrivals by a Poisson cluster process
• Lower limits and equivalences for convolution tails
• Convolution equivalence and distributions of random sums
• Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications
• On lower limits and equivalences for distribution tails of randomly stopped sums
• On convolution tails
• Limits of ratios of tails of measures
• Asymptotics for sums of random variables with local subexponential behaviour
• The closure of the convolution equivalent distribution class under convolution roots with applications to random sums
• Convolution equivalence and infinite divisibility

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