Convex minorants and the fluctuation theory of L\'evy processes

zbMath1492.60130arXiv2105.15060MaRDI QIDQ5094002

Aleksandar Mijatović, Jorge Ignacio González Cázares

Publication date: 2 August 2022

Full work available at URL: https://arxiv.org/abs/2105.15060

zbMATH Keywords

Lévy processesfluctuation theoryconvex minorantpiecewise linear convex functionsvertex process

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51)

Related Items (5)

Markovian structure in the concave majorant of Brownian motion ⋮ Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation ⋮ How smooth can the convex hull of a Lévy path be? ⋮ Asymptotic shape of the concave majorant of a Lévy process ⋮ Hölder continuity of the convex minorant of a Lévy process

Cites Work

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• On the law of the supremum of Lévy processes
• Convex minorants of random walks and Lévy processes
• The convex minorant of a Lévy process
• Fluctuation theory for Lévy processes. Ecole d'Eté de probabilités de Saint-Flour XXXV -- 2005.
• The concave majorant of Brownian motion
• Introductory lectures on fluctuations of Lévy processes with applications.
• Concave Majorants of Random Walks and Related Poisson Processes
• The Strong Law of Large Numbers When the Mean is Undefined

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