Subexponentiality and infinite divisibility
From MaRDI portal
Publication:4181024
DOI10.1007/BF00535504zbMath0397.60024OpenAlexW2079176310MaRDI QIDQ4181024
Paul Embrechts, Noël Veraverbeke, Charles M. Goldie
Publication date: 1979
Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00535504
Compound PoissonInfinite DivisibilityLognormal DistributionClosure PropertiesFactorization PropertiesRegular VariationSubexponential
Related Items (only showing first 100 items - show all)
ON PORTFOLIO SELECTION UNDER EXTREME RISK MEASURE: THE HEAVY-TAILED ICA MODEL ⋮ Subexponential potential asymptotics with applications ⋮ On infinitely divisible semimartingales ⋮ Convolutions of Long-Tailed and Subexponential Distributions ⋮ On max-sum equivalence and convolution closure of heavy-tailed distributions and their applications ⋮ Convolution equivalence and infinite divisibility ⋮ On moments and tail behaviors of storage processes ⋮ Modelling of extremal events in insurance and finance ⋮ Lévy-Type Stochastic Integrals with Regularly Varying Tails ⋮ SECOND ORDER SUBEXPONENTIALITY AND INFINITE DIVISIBILITY ⋮ Extremes of autoregressive threshold processes ⋮ Asymptotics for the moments of the overshoot and undershoot of a random walk ⋮ Externalities in the M/G/1 queue: LCFS-PR versus FCFS ⋮ A Conversation With Paul Embrechts ⋮ Exponential densities and compound Poisson measures ⋮ A NOTE ON THE CLOSURE OF CONVOLUTION POWER MIXTURES (RANDOM SUMS) OF EXPONENTIAL DISTRIBUTIONS ⋮ Subexponentialiy of densities of infinitely divisible distributions ⋮ Asymptotic Results for the Severity and Surplus Before Ruin for a Class of Lévy Insurance Processes ⋮ A new shape of extremal clusters for certain stationary semi-exponential processes with moderate long range dependence ⋮ The Markov branching process with density-independent catastrophes I. Behaviour of extinction probabilities ⋮ Asymptotic distributions of the overshoot and undershoots for the Lévy insurance risk process in the Cramér and convolution equivalent cases ⋮ Moment and MGF convergence of overshoots and undershoots for Lévy insurance risk processes ⋮ Asymptotics for the tail probability of random sums with a heavy-tailed random number and extended negatively dependent summands ⋮ Heavy-tailed asymptotics of stationary probability vectors of Markov chains of gi/g/1 type ⋮ Regularly distributed randomly stopped sum, minimum, and maximum ⋮ Tails in generalized Jackson networks with subexponential service-time distributions ⋮ Spatial asymptotics at infinity for heat kernels of integro-differential operators ⋮ Finite-time ruin probabilities under large-claim reinsurance treaties for heavy-tailed claim sizes ⋮ Local Time Asymptotics for Centered Lévy Processes with Two-Sided Reflection ⋮ Note on the Tail Behavior of Random Walk Maxima with Heavy Tails and Negative Drift ⋮ Asymptotics for the First Passage Times of Lévy Processes and Random Walks ⋮ Asymptotic expansions for infinite weighted convolutions of rapidly varying subexponential distributions ⋮ Maxima of Sums of Heavy-Tailed Random Variables ⋮ Joint exceedances of the ARCH process ⋮ Tail asymptotics for exponential functionals of Lévy processes ⋮ Nonexponential asymptotics for the solutions of renewal equations, with applications ⋮ Unnamed Item ⋮ Asymptotic Expansions for Distributions of Compound Sums of Random Variables with Rapidly Varying Subexponential Distribution ⋮ Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities ⋮ The finite-time ruin probability of the compound Poisson model with constant interest force ⋮ The distribution and asympotic behaviour of the negative Wiener–Hopf factor for Lévy processes with rational positive jumps ⋮ Lévy Processes with Two-Sided Reflection ⋮ Asymptotics for solutions of a defective renewal equation with applications ⋮ Transience and Recurrence of Markov Processes with Constrained Local Time ⋮ On regular variation for infinitely divisible random vectors and additive processes ⋮ The closure of a local subexponential distribution class under convolution roots, with applications to the compound Poisson process ⋮ The total claims distribution under inflationary conditions ⋮ Tail behavior of negatively associated heavy-tailed sums ⋮ On extreme ruinous behaviour of Lévy insurance risk processes ⋮ On subordinated distributions and random record processes ⋮ Infinite divisibility and generalized subexponentiality ⋮ General inverse problems for regular variation ⋮ Multivariate subexponential distributions and random sums of random vectors ⋮ Functions of discrete probability measures: Rates of convergence in the renewal theorem ⋮ Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions. ⋮ Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks. ⋮ A TANDEM QUEUE WITH LÉVY INPUT: A NEW REPRESENTATION OF THE DOWNSTREAM QUEUE LENGTH ⋮ Risk processes perturbed by α-stable Lévy motion ⋮ Ruin problem and how fast stochastic processes mix ⋮ Tail probabilities of subadditive functionals of Lévy processes. ⋮ Extremes of subexponential Lévy-driven random fields in the Gumbel domain of attraction ⋮ Passage time and fluctuation calculations for subexponential Lévy processes ⋮ Subexponential densities of infinitely divisible distributions on the half-line ⋮ Multivariate subexponential distributions and their applications ⋮ Second-order behaviour for self-decomposable distributions with two-sided regularly varying densities ⋮ The structure of the class of subexponential distributions ⋮ Some fractal sets determined by stable processes ⋮ Some asymptotic results useful in enumeration problems ⋮ Large claims approximations for risk processes in a Markovian environment ⋮ Functionals of infinitely divisible stochastic processes with exponential tails ⋮ Association of infinitely divisible random vectors ⋮ On the closure under infinitely divisible distribution roots ⋮ On the supremum of an infinitely divisible process ⋮ On directional convolution equivalent densities ⋮ Extremes of Lévy-driven spatial random fields with regularly varying Lévy measure ⋮ Quasi-stationary distributions for Lévy processes ⋮ Sample quantiles of heavy tailed stochastic processes ⋮ Randomly stopped sums with consistently varying distributions ⋮ Sample function behavior of increasing processes of class \(L\) ⋮ Ruin estimates for large claims ⋮ Banach algebras of measures of class S(\(\gamma\) ) ⋮ Tails of subordinated laws: The regularly varying case ⋮ Random walks with non-convolution equivalent increments and their applications ⋮ The Gerber-Shiu expected discounted penalty function for Lévy insurance risk processes ⋮ Subexponential distribution functions in \(R^{d}\) ⋮ Extremal behavior of stochastic integrals driven by regularly varying Lévy processes ⋮ Stable Lévy motion approximation in collective risk theory ⋮ The queue length in an \(M/G/1\) batch arrival retrial queue ⋮ A note on max-sum equivalence ⋮ Asymptotics of random sums of negatively dependent random variables in the presence of dominatedly varying tails ⋮ A new class of large claim size distributions: definition, properties, and ruin theory ⋮ Local subexponentiality and self-decomposability ⋮ On asymptotic equivalence among the solutions of some defective renewal equations ⋮ Sample path large deviations for Lévy processes and random walks with regularly varying increments ⋮ On a closure property of convolution equivalent class of distributions ⋮ On closure properties of heavy-tailed distributions for random sums ⋮ The Wiener condition and the conjectures of Embrechts and Goldie ⋮ Tail behavior of random sums of negatively associated increments ⋮ Convolution and convolution-root properties of long-tailed distributions ⋮ Asymptotics of randomly stopped sums in the presence of heavy tails
Cites Work
- Unnamed Item
- Unnamed Item
- A general result on infinite divisibility
- Asymptotic behaviour of Wiener-Hopf factors of a random walk
- The class of subexponential distributions
- Degeneracy properties of subcritical branching processes
- Functions of probability measures
- One-sided analogues of Karamata's regular variation
- On the tails of waiting-time distributions
- On the infinite divisibility of the lognormal distribution
- Subexponential distributions and dominated-variation tails
- On the Asymptotic Behavior of a Class of Infinitely Divisible Laws
- A Lemma on regular variation of a transient renewal function
- Some results on regular variation for distributions in queueing and fluctuation theory
- Regular variation of the tail of a subordinated probability distribution
This page was built for publication: Subexponentiality and infinite divisibility