Hermite variations of the fractional Brownian sheet
Please always quote using this URN:urn:nbn:de:0296-matheon-7232
- We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet $W^{\alpha, \beta}$ with Hurst parameter $(\alpha, \beta) \in (0,1)2$. When $0<\alpha \leq 1-\frac{1}{2q}$ or $0<\beta \leq 1-\frac{1}{2q}$ a central limit theorem holds for the renormalized Hermite variations of order $q\geq 2$, while for $1-\frac{1}{2q}<\alpha, \beta < 1$ we prove that these variations satisfy a non-central limit theorem. In fact, they converge to a random variable which is the value of a two-parameter Hermite process at time $(1,1)$.
Author: | Anthony Réveillac, Michael Stauch, Ciprian Tudor |
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URN: | urn:nbn:de:0296-matheon-7232 |
Referee: | Dirk Becherer |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2010/06/10 |
Release Date: | 2010/06/10 |
Institute: | Humboldt-Universität zu Berlin |
Preprint Number: | 728 |