Convolution equivalence and infinite divisibility
From MaRDI portal
Publication:4819467
DOI10.1239/jap/1082999075zbMath1051.60019OpenAlexW2097360682MaRDI QIDQ4819467
Publication date: 24 September 2004
Published in: Journal of Applied Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1239/jap/1082999075
Infinitely divisible distributions; stable distributions (60E07) Limit theorems in probability theory (60F99)
Related Items (96)
Sample paths of a Lévy process leading to first passage over high levels in finite time ⋮ Extremes of subexponential Lévy-driven random fields in the Gumbel domain of attraction ⋮ Extreme value theory for spatial random fields -- with application to a Lévy-driven field ⋮ Passage time and fluctuation calculations for subexponential Lévy processes ⋮ Subexponential densities of infinitely divisible distributions on the half-line ⋮ Large Deviations of a Sum of Independent Random Variables with Distributions with Rapidly Decreasing Tails ⋮ Second-order behaviour for self-decomposable distributions with two-sided regularly varying densities ⋮ Asymptotics of convolution with the semi-regular-variation tail and its application to risk ⋮ On the closure under infinitely divisible distribution roots ⋮ On directional convolution equivalent densities ⋮ Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure ⋮ On convolution equivalence with applications ⋮ SECOND ORDER SUBEXPONENTIALITY AND INFINITE DIVISIBILITY ⋮ Extremes of autoregressive threshold processes ⋮ Asymptotics for the moments of the overshoot and undershoot of a random walk ⋮ On the Maximum Exceedance of a Sequence of Random Variables Over a Renewal Threshold ⋮ The overshoot of a random walk with negative drift ⋮ Convolution equivalent Lévy processes and first passage times ⋮ Random walks with non-convolution equivalent increments and their applications ⋮ Lower limits and equivalences for convolution tails ⋮ 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 ⋮ Randomly weighted sums of dependent subexponential random variables with applications to risk theory ⋮ Tail asymptotics for exponential functionals of Lévy processes: the convolution equivalent case ⋮ Local subexponentiality and self-decomposability ⋮ ASYMPTOTICS FOR A DISCRETE-TIME RISK MODEL WITH THE EMPHASIS ON FINANCIAL RISK ⋮ On a closure property of convolution equivalent class of distributions ⋮ The Wiener condition and the conjectures of Embrechts and Goldie ⋮ Insensitivity to Negative Dependence of Asymptotic Tail Probabilities of Sums and Maxima of Sums ⋮ Tail behavior of random sums of negatively associated increments ⋮ Extremes of Lévy driven mixed MA processes with convolution equivalent distributions ⋮ Exponential densities and compound Poisson measures ⋮ Asymptotic results on tail moment for light-tailed risks ⋮ Ruin under light-tailed or moderately heavy-tailed insurance risks interplayed with financial risks ⋮ Subexponentialiy of densities of infinitely divisible distributions ⋮ Implicit renewal theory for exponential functionals of Lévy processes ⋮ Tail behaviors of semi-stable distributions ⋮ Path decomposition of ruinous behavior for a general Lévy insurance risk process ⋮ Some properties of the exponential distribution class with applications to risk theory ⋮ ECOMOR and LCR reinsurance with gamma-like claims ⋮ Asymptotics for the tail probability of random sums with a heavy-tailed random number and extended negatively dependent summands ⋮ Asymptotics for the solutions to defective renewal equations ⋮ Asymptotic aspects of the Gerber-Shiu function in the renewal risk model using Wiener-Hopf factorization and convolution equivalence ⋮ Extremes of aggregated Dirichlet risks ⋮ Spatial asymptotics at infinity for heat kernels of integro-differential operators ⋮ Applications of factorization embeddings for Lévy processes ⋮ The subexponentiality of products revisited ⋮ THE SUBEXPONENTIAL PRODUCT CONVOLUTION OF TWO WEIBULL-TYPE DISTRIBUTIONS ⋮ Convolution equivalence and distributions of random sums ⋮ On large deviations of a sum of independent random variables with rapidly decreasing distribution tails ⋮ On asymptotic behavior of the convolution of distributions with regularly exponentially decreasing tails ⋮ Asymptotics for the finite-time ruin probability in a discrete-time risk model with dependent insurance and financial risks ⋮ Asymptotics for the First Passage Times of Lévy Processes and Random Walks ⋮ Estimates for the finite-time ruin probability with insurance and financial risks ⋮ Firm growth and Laplace distribution: the importance of large jumps ⋮ The Uniform Asymptotics of the Overshoot of a Random Walk with Light-Tailed Increments ⋮ 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 ⋮ On a class of Lévy processes ⋮ Ruin probabilities and overshoots for general Lévy insurance risk processes ⋮ The closure of the convolution equivalent distribution class under convolution roots with applications to random sums ⋮ A note on the tail behavior of randomly weighted sums with convolution-equivalently distributed random variables ⋮ Lower limits and upper limits for tails of random sums supported on \(\mathbb R\) ⋮ From light tails to heavy tails through multiplier ⋮ Excursion sets of infinitely divisible random fields with convolution equivalent Lévy measure ⋮ Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries ⋮ Extremes of subexponential Lévy driven moving average processes ⋮ Tail asymptotics under beta random scaling ⋮ Two hypotheses on the exponential class in the class of \(O\)-subexponential infinitely divisible distributions ⋮ Some new equivalent conditions on asymptotics and local asymptotics for random sums and their applications ⋮ Extremal dependence of random scale constructions ⋮ Tail behavior of the sums of dependent and heavy-tailed random variables ⋮ On the asymptotic behaviour of Lévy processes. I: Subexponential and exponential processes ⋮ On lower limits and equivalences for distribution tails of randomly stopped sums ⋮ Interplay of insurance and financial risks in a discrete-time model with strongly regular variation ⋮ Tail asymptotics for the supremum of an infinitely divisible field with convolution equivalent Lévy measure ⋮ Reinsurance under the LCR and ECOMOR treaties with emphasis on light-tailed claims ⋮ On a generic class of two-node queueing systems ⋮ The uniform local asymptotics for a Lévy process and its overshoot and undershoot ⋮ Tail asymptotics of an infinitely divisible space-time model with convolution equivalent Lévy measure ⋮ Self-decomposable laws from continuous branching processes ⋮ Randomly stopped minima and maxima with exponential-type distributions ⋮ Equivalent conditions of asymptotics for the density of the supremum of a random walk in the Intermediate case ⋮ Heavy tails of a Lévy process and its maximum over a random time interval ⋮ Minimum of Dependent Random Variables with Convolution-Equivalent Distributions ⋮ Some positive conclusions related to the Embrechts-Goldie conjecture ⋮ A Lévy Process Reflected at a Poisson Age Process ⋮ Path decomposition of a reflected Lévy process on first passage over high levels ⋮ Tail behavior of negatively associated heavy-tailed sums ⋮ Extremes of the stochastic heat equation with additive Lévy noise ⋮ Tails of Stopped Random Products: The Factoid and Some Relatives ⋮ Embrechts-Goldie's problem on the class of lattice convolution equivalent distributions ⋮ Exact upper tail probabilities of random series ⋮ The product distribution of dependent random variables with applications to a discrete-time risk model ⋮ Sample path behavior of a Lévy insurance risk process approaching ruin, under the Cramér-Lundberg and convolution equivalent conditions
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Asymptotics of infinitely divisible distributions on \({\mathbb{R}}\)
- Convolution tails, product tails and domains of attraction
- On the supremum of an infinitely divisible process
- On convolution tails
- Generalized gamma convolutions and related classes of distributions and densities
- The class of subexponential distributions
- Degeneracy properties of subcritical branching processes
- The maximum on a random time interval of a random walk with long-tailed increments and negative drift.
- Appendix: A primer on heavy-tailed distributions
- Subexponential distributions and integrated tails
- Subexponentiality and infinite divisibility
- On the Asymptotics of the Density of an Infinitely Divisible Distribution at Infinity
- Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy Flight
- On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications
- Regular variation of the tail of a subordinated probability distribution
This page was built for publication: Convolution equivalence and infinite divisibility