Zooming in on a Lévy process at its supremum

DOI10.1214/17-AAP1320zbMath1391.60107arXiv1610.04471MaRDI QIDQ1650094

Jevgenijs Ivanovs

Publication date: 29 June 2018

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

Full work available at URL: https://arxiv.org/abs/1610.04471

zbMATH Keywords

self-similarityinvariance principlefunctional limit theoremdiscretization errorEuler schemescaling limitsdomains of attractionmixing convergenceconditioned to stay positivehigh frequency statisticssmall-time behaviour

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52) Functional limit theorems; invariance principles (60F17)

Related Items (15)

Optimal estimation of the supremum and occupation times of a self-similar Lévy process ⋮ Geometrically Convergent Simulation of the Extrema of Lévy Processes ⋮ Intermittency in the small-time behavior of Lévy processes ⋮ Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation ⋮ On the speed of convergence of Piterbarg constants ⋮ How smooth can the convex hull of a Lévy path be? ⋮ On the divergence and vorticity of vector ambit fields ⋮ Extreme order statistics of random walks ⋮ Lévy processes conditioned to stay in a half-space with applications to directional extremes ⋮ A Monte Carlo algorithm for the extrema of tempered stable processes ⋮ Zooming-in on a Lévy process: failure to observe threshold exceedance over a dense grid ⋮ Limit theorems for trawl processes ⋮ A broad view of queueing theory through one issue ⋮ Discretization error for a two-sided reflected Lévy process ⋮ Discretization of the Lamperti representation of a positive self-similar Markov process

Uses Software

• GAUSSIAN

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