The asymptotic behavior of densities related to the supremum of a stable process

DOI10.1214/09-AOP479zbMath1185.60052arXiv1001.4872MaRDI QIDQ2268702

Mladen Svetoslavov Savov, Ronald Arthur Doney

Publication date: 8 March 2010

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.4872

zbMATH Keywords

asymptotic behaviorstable processsupremumpassage time densitystable meander

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Strong limit theorems (60F15) Stable stochastic processes (60G52) Distribution theory (60E99)

Related Items (21)

On the one dimensional spectral heat content for stable processes ⋮ Optimal estimation of the supremum and occupation times of a self-similar Lévy process ⋮ Fluctuation theory for Lévy processes with completely monotone jumps ⋮ The first passage time of a stable process conditioned to not overshoot ⋮ Infinite random planar maps related to Cauchy processes ⋮ Bernstein-gamma functions and exponential functionals of Lévy processes ⋮ On the law of the supremum of Lévy processes ⋮ Asymptotic behaviour of first passage time distributions for Lévy processes ⋮ Local behaviour of first passage probabilities ⋮ Local limit theorem for the maximum of asymptotically stable random walks ⋮ Penalisation of a stable Lévy process involving its one-sided supremum ⋮ Zooming-in on a Lévy process: failure to observe threshold exceedance over a dense grid ⋮ \(\varepsilon\)-strong simulation of the convex minorants of stable processes and meanders ⋮ On the supremum of products of symmetric stable processes ⋮ Spectral analysis of stable processes on the positive half-line ⋮ Hitting densities for spectrally positive stable processes ⋮ On extrema of stable processes ⋮ Asymptotically stable random walks of index \(1 < \alpha < 2\) killed on a finite set ⋮ Density behaviour related to Lévy processes ⋮ A lifetime of excursions through random walks and Lévy processes ⋮ On Doney's striking factorization of the arc-sine law

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• A new fluctuation identity for Lévy processes and some applications

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