Random integral representations for free-infinitely divisible and tempered stable distributions

DOI10.1016/J.SPL.2006.08.009zbMath1112.60007arXiv1206.3044OpenAlexW1979969708MaRDI QIDQ876986

Zbigniew J. Jurek

Publication date: 19 April 2007

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

Full work available at URL: https://arxiv.org/abs/1206.3044

zbMATH Keywords

Lévy processLévy-Khintchine formulastable measures\(\lambda\)-mixturesfree-infinite divisibilityHilbert and Banach spacesinfinite divisible measureLévy spectral measuretempered stable measures

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Processes with independent increments; Lévy processes (60G51) Characteristic functions; other transforms (60E10) Free probability and free operator algebras (46L54) Probability theory on linear topological spaces (60B11)

Related Items (7)

Exponential bounds of ruin probabilities for non-homogeneous risk models ⋮ On a method of introducing free-infinitely divisible probability measures ⋮ Remarks on compositions of some random integral mappings ⋮ The random integral representation conjecture: a quarter of a century later ⋮ Unnamed Item ⋮ Remarks on restricted Nevanlinna transforms ⋮ Inversions of Lévy measures and the relation between long and short time behavior of Lévy processes

Cites Work

• Self-decomposability and Lévy processes in free probability
• Relations between the \(\epsilon\)-selfdecomposable and selfdecomposable measures
• Random integral representations for classes of limit distributions similar to Lévy class \(L_ 0\)
• Stable laws and domains of attraction in free probability theory
• An integral representation for selfdecomposable banach space valued random variables
• Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Lévy Flight
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