A central limit theorem for a weighted power variation of a Gaussian process*

被引:0
|
作者
Raimondas Malukas
Rimas Norvaiša
机构
[1] Vilnius University,Institute of Mathematics and Informatics
来源
Lithuanian Mathematical Journal | 2014年 / 54卷
关键词
weighted power variation; central limit theorem; Gaussian processes; locally stationary increments; bifractional Gaussian process; subfractional Gaussian process; 60G15; 60G22; 60F05;
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学科分类号
摘要
Let ρ be a real-valued function on [0, T], and let LSI(ρ) be a class of Gaussian processes over time interval [0, T], which need not have stationary increments but their incremental variance σ(s, t) is close to the values ρ(|t − s|) as t → s uniformly in s ∈ (0, T]. For a Gaussian processesGfrom LSI(ρ), we consider a power variation Vn corresponding to a regular partition πn of [0, T] and weighted by values of ρ(·). Under suitable hypotheses on G, we prove that a central limit theorem holds for Vn as the mesh of πn approaches zero. The proof is based on a general central limit theorem for random variables that admit a Wiener chaos representation. The present result extends the central limit theorem for a power variation of a class of Gaussian processes with stationary increments and for bifractional and subfractional Gaussian processes.
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页码:323 / 344
页数:21
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