On a new Class of Tempered Stable Distributions: Moments and Regular Variation

DOI10.1239/jap/1354716655zbMath1269.60018arXiv1109.1028OpenAlexW2034010887MaRDI QIDQ4903040

Michael Grabchak

Publication date: 19 January 2013

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.1028

zbMATH Keywords

regular variationdomain of attractiontail behaviourtempered stable distributioninfinite divisible lawRosiński measure

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51)

Related Items (15)

On the consistency of the MLE for Ornstein-Uhlenbeck and other selfdecomposable processes ⋮ Limit theorems and phase transitions for two models of summation of iid random variables depending on parameters ⋮ On the simulation of general tempered stable Ornstein–Uhlenbeck processes ⋮ Does value-at-risk encourage diversification when losses follow tempered stable or more general Lévy processes? ⋮ Modelling tail risk with tempered stable distributions: an overview ⋮ Simulation of Tempered Stable Lévy Bridges and Its Applications ⋮ An exact method for simulating rapidly decreasing tempered stable distributions in the finite variation case ⋮ Domains of attraction for positive and discrete tempered stable distributions ⋮ On the transition laws of \(p\)-tempered \(\alpha \)-stable OU-processes ⋮ Estimation and simulation for multivariate tempered stable distributions ⋮ Rejection sampling for tempered Lévy processes ⋮ Limit Theorems and Phase Transitions for Two Models of Summation of Independent Identically Distributed Random Variables with a Parameter ⋮ Efficient simulation of \(p\)-tempered \(\alpha\)-stable OU processes ⋮ Inversions of Lévy measures and the relation between long and short time behavior of Lévy processes ⋮ Discussion of `On simulation and properties of the stable law' by Devroye and James

Cites Work

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• Moment properties of multivariate infinitely divisible laws and criteria for multivariate self-decomposability
• Some classes of multivariate infinitely divisible distributions admitting stochastic integral representations
• Tempering stable processes
• A note on new classes of infinitely divisible distributions on \(\mathbb{R}^{d}\)
• Modelling heterogeneity in survival analysis by the compound Poisson distribution
• A characterization of multivariate regular variation.
• A subclass of type \(G\) selfdecomposable distributions on \(\mathbb R^d\)
• Tempered Infinitely Divisible Distributions and Processes
• Do financial returns have finite or infinite variance? A paradox and an explanation
• Cumulants of infinitely divisible distributions
• Generalized tempered stable processes
• Modelling Cell Generation Times by Using the Tempered Stable Distribution
• Chance and Stability
• On regular variation for infinitely divisible random vectors and additive processes

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