Behavior of the Hermite sheet with respect to the Hurst index

DOI10.1016/j.spa.2018.07.017zbMath1451.60052OpenAlexW2886950120MaRDI QIDQ2000160

Ciprian A. Tudor, Héctor Araya

Publication date: 28 June 2019

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2018.07.017

zbMATH Keywords

convergencecumulantsfractional Brownian motionself-similarityRosenblatt processHurst indexWiener chaosmultiple stochastic integralsHermite processmultiparameter stochastic processes

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (3)

Rosenblatt Laplace motion ⋮ Limit behavior of the Rosenblatt Ornstein–Uhlenbeck process with respect to the Hurst index ⋮ Behavior with respect to the Hurst index of the Wiener Hermite integrals and application to SPDEs

Cites Work

• Functional limit theorems for generalized variations of the fractional Brownian sheet
• Properties and numerical evaluation of the Rosenblatt distribution
• Selected aspects of fractional Brownian motion.
• Structure of the third moment of the generalized Rosenblatt distribution
• Wiener integrals with respect to the Hermite random field and applications to the wave equation
• Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
• Central limit theorems for non-linear functionals of Gaussian fields
• Noncentral limit theorem for the generalized Hermite process
• Behavior of the generalized Rosenblatt process at extreme critical exponent values
• Central limit theorems for sequences of multiple stochastic integrals
• Analysis of Variations for Self-similar Processes
• Normal Approximations with Malliavin Calculus
• HERMITE VARIATIONS OF THE FRACTIONAL BROWNIAN SHEET
• The Malliavin Calculus and Related Topics
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields
• Limit behavior of the Rosenblatt Ornstein–Uhlenbeck process with respect to the Hurst index
• Long-Range Dependence and Self-Similarity
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications

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