Derivatives of sup-functionals of fractional Brownian motion evaluated at \(H=\frac{1}{2}\)

DOI10.1214/22-EJP848MaRDI QIDQ2082686

Krzysztof Bisewski, Tomasz Rolski, Krzysztof Dȩbicki

Publication date: 4 October 2022

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.08788

zbMATH Keywords

fractional Brownian motionPickands constantPiterbarg constantWills functionalexpected workload

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Extreme value theory; extremal stochastic processes (60G70) Sample path properties (60G17)

Related Items (3)

Lower bound for the expected supremum of fractional brownian motion using coupling ⋮ On the Gaussian Volterra processes with power-type kernels ⋮ Derivative of the expected supremum of fractional Brownian motion at \(H=1\)

Uses Software

• Mathematica
• GAUSSIAN

Cites Work

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• On asymptotic constants in the theory of extremes for Gaussian processes
• Pickands' constant \(H_{\alpha}\) does not equal \(1/\Gamma(1/\alpha)\), for small \(\alpha\)
• The Wills functional and Gaussian processes
• A note on upper estimates for Pickands constants
• Extremes of a certain class of Gaussian processes
• New and refined bounds for expected maxima of fractional Brownian motion
• On generalised Piterbarg constants
• On the uniqueness of maximizers of Markov-Gaussian processes
• Discretization error in simulation of one-dimensional reflecting Brownian motion
• A continuous mapping theorem for the smallest argmax functional
• Approximation of supremum of max-stable stationary processes \& Pickands constants
• Exact simulation of Brown-Resnick random fields at a finite number of locations
• Queues and Lévy fluctuation theory
• Stochastic calculus for fractional Brownian motion and related processes.
• How rich is the class of multifractional Brownian motions?
• Bounds for expected maxima of Gaussian processes and their discrete approximations
• Density factorizations for brownian motion, meander and the three-dimensional bessel process, and applications
• Large Deviations for Gaussian Queues
• The joint density of the maximum and its location for a Wiener process with drift
• Simulation of the Asymptotic Constant in Some Fluid Models
• Stochastic properties of the linear multifractional stable motion
• Bounds for expected supremum of fractional Brownian motion with drift
• Pickands’ constant at first order in an expansion around Brownian motion
• Random Fields and Geometry
• PATH PROPERTIES OF THE LINEAR MULTIFRACTIONAL STABLE MOTION
• Fractional Brownian Motions, Fractional Noises and Applications
• A table of integrals of the Error functions

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