Wiener Integrals with Respect to the Hermite Process and a Non-Central Limit Theorem

DOI10.1080/07362990701540519zbMath1130.60061OpenAlexW2132036934MaRDI QIDQ5421607

Ciprian A. Tudor, Makoto Maejima

Publication date: 24 October 2007

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

Full work available at URL: https://doi.org/10.1080/07362990701540519

zbMATH Keywords

fractional Brownian motionOrnstein-Uhlenbeck processWiener integralnon-central limit theoremHermite process

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stochastic integrals (60H05) Self-similar stochastic processes (60G18)

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Cites Work

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• Functional limit theorems for weighted sums of i.i.d. random variables
• Weighted sums of i.i.d. random variables attracted to integrals of stable processes
• Stochastic analysis of the fractional Brownian motion
• On extremal theory for self-similar processes
• Wavelet-type expansion of the Rosenblatt process
• A note on Rosenblatt distributions
• Convergence of weighted sums of random variables with long-range dependence.
• Wavelet-based simulation of fractional Brownian motion revisited
• Weak convergence to fractional brownian motion and to the rosenblatt process
• Convergence of integrated processes of arbitrary Hermite rank
• Non-central limit theorems for non-linear functional of Gaussian fields
• Stochastic Calculus for Fractional Brownian Motion I. Theory
• The Invariance Principle for Stationary Processes
• Stochastic calculus with respect to Gaussian processes

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