Bounds for expected maxima of Gaussian processes and their discrete approximations

DOI10.1080/17442508.2015.1126282zbMath1361.60027arXiv1508.00099OpenAlexW2964159591MaRDI QIDQ2974854

Konstantin A. Borovkov, Yuliya S. Mishura, Mikhail Zhitlukhin, Alexander Novikov

Publication date: 11 April 2017

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.00099

zbMATH Keywords

fractional Brownian motionGaussian processesdiscrete approximationlong memory processesexpected maximum

Mathematics Subject Classification ID

Gaussian processes (60G15) Fractional processes, including fractional Brownian motion (60G22) Extreme value theory; extremal stochastic processes (60G70) Brownian motion (60J65)

Related Items (17)

Bounds for the expected supremum of some non-stationary Gaussian processes ⋮ New and refined bounds for expected maxima of fractional Brownian motion ⋮ Asymptotics of running maxima for \(\varphi \)-subgaussian random double arrays ⋮ Simulation paradoxes related to a fractional Brownian motion with small Hurst index ⋮ High excursions of Gaussian nonstationary processes in discrete time ⋮ Gaussian Volterra processes: Asymptotic growth and statistical estimation ⋮ On the speed of convergence of Piterbarg constants ⋮ Entropy and alternative entropy functionals of fractional Gaussian noise as the functions of Hurst index ⋮ Lower bound for the expected supremum of fractional brownian motion using coupling ⋮ Restoration of well-posedness of infinite-dimensional singular ODE's via noise ⋮ Fractional Ornstein-Uhlenbeck process with stochastic forcing, and its applications ⋮ On the maximum of the discretely sampled fractional Brownian motion with small Hurst parameter ⋮ More on maximal inequalities for sub-fractional Brownian motion ⋮ Bounds for expected supremum of fractional Brownian motion with drift ⋮ Derivatives of sup-functionals of fractional Brownian motion evaluated at \(H=\frac{1}{2}\) ⋮ Derivative of the expected supremum of fractional Brownian motion at \(H=1\) ⋮ On density functions related to discrete time maximum of some one-dimensional diffusion processes

Cites Work

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• Corrected diffusion approximations in certain random walk problems
• Some comparisons for Gaussian processes
• The Generic Chaining
• Upper and Lower Bounds for Stochastic Processes
• Sequential Tests for the Mean of a Normal Distribution IV (Discrete Case)

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