Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion
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Publication:2519679
DOI10.1214/07-AOP385zbMath1155.60010arXiv0705.0570OpenAlexW4296024135MaRDI QIDQ2519679
Publication date: 27 January 2009
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0705.0570
fractional Brownian motionMalliavin calculusexact rate of convergenceweighted quadratic variationBreuer and Major theoremweighted cubic variation
Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stochastic calculus of variations and the Malliavin calculus (60H07)
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Cites Work
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- Central and non-central limit theorems for weighted power variations of fractional Brownian motion
- Power variation of some integral fractional processes
- Limits for weighted \(p\)-variations and likewise functionals of fractional diffusions with drift
- Weighted power variations of iterated Brownian motion
- Central limit theorems for non-linear functionals of Gaussian fields
- Generalized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index \(H\geq\frac 1 4\).
- Variations of the solution to a stochastic heat equation
- Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion
- CLT and other limit theorems for functionals of Gaussian processes
- Convergence of integrated processes of arbitrary Hermite rank
- Non-central limit theorems for non-linear functional of Gaussian fields
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