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Berry-Esséen bounds and almost sure CLT for the quadratic variation of a class of Gaussian process.
- Source :
-
Communications in Statistics: Theory & Methods . 2024, Vol. 53 Issue 11, p3920-3939. 20p. - Publication Year :
- 2024
-
Abstract
- We propose a condition which is valid for a class of continuous Gaussian processes that may fail to be self-similar or have stationary increments. Some examples include the sub-fractional Brownian motion and the bi-fractional Brownian motion and the sub-bifractional Brownian motion. Under this assumption, we show an upper bound for the difference between the inner product associated with a class of Gaussian process and that associated with the fractional Brownian motion. This inequality relates a class of Gaussian processes to the well studied fractional Brownian motion, which characterizes their relationship quantitatively. As an application, we obtain the optimal Berry-Esséen bounds for the quadratic variation when H ∈ (0 , 2 3 ] and the upper Berry-Esséen bounds when H ∈ (2 3 , 3 4 ]. As a by-product, we also show the almost sure central limit theorem (ASCLT) for the quadratic variation when H ∈ (0 , 3 4 ]. The results in the present paper extend and improve those in the literature. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GAUSSIAN processes
*BROWNIAN motion
*CENTRAL limit theorem
*CONTINUOUS processing
Subjects
Details
- Language :
- English
- ISSN :
- 03610926
- Volume :
- 53
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Communications in Statistics: Theory & Methods
- Publication Type :
- Academic Journal
- Accession number :
- 176582855
- Full Text :
- https://doi.org/10.1080/03610926.2023.2167055