Mittag-Leffler functions and stable Lévy processes without negative jumps

DOI10.1016/j.exmath.2009.12.002zbMath1194.33022OpenAlexW2963207619MaRDI QIDQ984629

Thomas Simon

Publication date: 20 July 2010

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2009.12.002

zbMATH Keywords

Mittag-Leffler functionLévy processesWiener-Hopf factorization

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Mittag-Leffler functions and generalizations (33E12) Stable stochastic processes (60G52)

Related Items (8)

Reflected spectrally negative stable processes and their governing equations ⋮ Law of the first passage triple of a spectrally positive strictly stable process ⋮ Intertwining certain fractional derivatives ⋮ On \(1/f\) noise ⋮ On exit time of stable processes ⋮ On the law of homogeneous stable functionals ⋮ Hitting densities for spectrally positive stable processes ⋮ Mittag-Leffler functions and complete monotonicity

Cites Work

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• The law of the supremum of a stable Lévy process with no negative jumps
• A few remarks on the supremum of stable processes
• On Wiener-Hopf factorisation and the distribution of extrema for certain stable processes
• On Mittag-Leffler-type functions in fractional evolution processes
• Completely monotone generalized Mittag-Leffler functions
• Introductory lectures on fluctuations of Lévy processes with applications.
• On the Maxima of Random Walks and Stable Processes and the Arc-Sine Law
• Symmetric stable processes, fubinfs theorem, and some extensions of the ciesielski-taylor identities in law
• On the First Exit Time of a Completely Asymmetric Stable Process from a Finite Interval
• Maxima of sums of random variables and suprema of stable processes
• The completely monotonic character of the Mittag-Leffler function 𝐸ₐ(-𝑥)
• The representation of 𝑒^{-𝑥^{𝜆}} as a Laplace integral

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