The full solution of the convolution closure problem for convolution- equivalent distributions
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Publication:808082
DOI10.1016/0022-247X(91)90291-7zbMath0731.60013MaRDI QIDQ808082
Claudia Klüppelberg, José A. Villaseñor
Publication date: 1991
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Related Items (21)
On the non-closure under convolution for strong subexponential distributions ⋮ Some discussions on the local distribution classes ⋮ Estimates for the overshoot of a random walk with negative drift and non-convolution equivalent increments ⋮ Renewal theory for random variables with a heavy tailed distribution and finite variance ⋮ On a closure property of convolution equivalent class of distributions ⋮ Convolution and convolution-root properties of long-tailed distributions ⋮ Subexponentialiy of densities of infinitely divisible distributions ⋮ The local asymptotic estimation for the supremum of a random walk with generalized strong subexponential summands ⋮ Infinite-time absolute ruin in dependent renewal risk models with constant force of interest ⋮ Some properties of the exponential distribution class with applications to risk theory ⋮ Asymptotics for the solutions to defective renewal equations ⋮ Convolution equivalence and distributions of random sums ⋮ Ratio of the tail of an infinitely divisible distribution on the line to that of its Lévy measure ⋮ Tail behavior of supremum of a random walk when Cramér's condition fails ⋮ Two hypotheses on the exponential class in the class of \(O\)-subexponential infinitely divisible distributions ⋮ Tail behavior of the sums of dependent and heavy-tailed random variables ⋮ Asymptotic ordering of distribution functions and convolution semigroups ⋮ Some positive conclusions related to the Embrechts-Goldie conjecture ⋮ Infinite divisibility and generalized subexponentiality ⋮ Embrechts-Goldie's problem on the class of lattice convolution equivalent distributions ⋮ On a transformation between distributions obeying the principle of a single big jump
Cites Work
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- Convolution tails, product tails and domains of attraction
- On convolution tails
- Degeneracy properties of subcritical branching processes
- Subexponential distributions and characterizations of related classes
- Asymptotic ordering of distribution functions and convolution semigroups
- Functions of probability measures
- Subexponential distributions and integrated tails
- On the non-closure under convolution of the subexponential family
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