非高斯多参数埃尔米特随机场二次变分的渐近性质

IF 0.4 4区 数学 Q4 STATISTICS & PROBABILITY
T. T. Diu Tran
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引用次数: 0

摘要

令Zt q,H t∈[0,1]d表示阶为q≥1的d参数埃尔米特随机场,自相似参数H = H₁,…,Hd∈1 / 2,1d。这个过程是h自相似的,具有固定的增量,并表现出长期依赖性。具体的例子包括分数布朗运动q = 1, d = 1,分数布朗片q = 1, d≥2,Rosenblatt过程q = 2, d = 1以及Rosenblatt片q = 2, d≥2。对于任意q≥2,d≥1且H∈½,1d,我们证明了Zq,H的二次变分的适当重整化在L2Ω收敛于一个自相似指数H′= 1 + 2H−2/q的标准d参数Rosenblatt随机变量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic behavior for quadratic variations of non-Gaussian multiparameter Hermite random fields
Let Zt q,H t∈[0,1]d denote a d-parameter Hermite random field of order q ≥ 1 and self-similarity parameter H = H₁, . . . ,Hd ∈  ½, 1d. This process is H-self-similar, has stationary increments and exhibits long-range dependence. Particular examples include fractional Brownian motion q = 1, d = 1, fractional Brownian sheet q = 1, d ≥ 2, the Rosenblatt process q = 2, d = 1 as well as the Rosenblatt sheet q = 2, d ≥ 2. For any q ≥ 2, d ≥ 1 and H ∈ ½, 1d we show in this paper that a proper renormalization of the quadratic variation of Zq,H converges in L2Ω to a standard d-parameter Rosenblatt random variable with self-similarity index H' = 1 + 2H − 2/q.
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来源期刊
CiteScore
0.70
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.
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