Variations and estimators for self-similarity parameters via Malliavin calculus
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Publication:971934
DOI10.1214/09-AOP459zbMath1196.60036arXiv0709.3896OpenAlexW1634894495MaRDI QIDQ971934
Ciprian A. Tudor, Frederi G. Viens
Publication date: 17 May 2010
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0709.3896
Central limit and other weak theorems (60F05) Stochastic calculus of variations and the Malliavin calculus (60H07) Self-similar stochastic processes (60G18)
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Uses Software
Cites Work
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- Unnamed Item
- Convergence en loi des H-variations d'un processus gaussien stationnaire sur \({\mathbb{R}}\). (Convergence in law of H-variations of a stationary Gaussian process)
- Stein's method on Wiener chaos
- Limits for weighted \(p\)-variations and likewise functionals of fractional diffusions with drift
- Self-similarity in high-speed packet traffic: analysis and modeling of Ethernet traffic measurements
- Central limit theorems for multiple Skorokhod integrals
- Multivariate normal approximation using Stein's method and Malliavin calculus
- Error bounds on the non-normal approximation of Hermite power variations of fractional Brownian motion
- Weighted power variations of iterated Brownian motion
- Central limit theorems for non-linear functionals of Gaussian fields
- Stock market prices and long-range dependence
- Quadratic variations and estimation of the local Hölder index of a Gaussian process
- Limit theorems for the nonlinear functional of stationary Gaussian processes
- Renormalized self-intersection local time for fractional Brownian motion
- Variations of the solution to a stochastic heat equation
- Central limit theorems for multiple stochastic integrals and Malliavin calculus
- Central limit theorems for sequences of multiple stochastic integrals
- Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion
- The Malliavin Calculus and Related Topics
- 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
- Analysis of the Rosenblatt process
- Estimating the parameters of a fractional Brownian motion by discrete variations of its sample paths
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