HERMITE VARIATIONS OF THE FRACTIONAL BROWNIAN SHEET

被引：11
|
作者：
Reveillac, Anthony [1 ]
Stauch, Michael [1 ]
Tudor, Ciprian A. [2 ]
机构：
[1] Humboldt Univ, Inst Math, D-10099 Berlin, Germany
[2] Univ Lille 1, UFR Math, Lab Paul Painleve, F-59655 Villeneuve Dascq, France
来源：
STOCHASTICS AND DYNAMICS | 2012年 / 12卷 / 03期
基金：
奥地利科学基金会;
关键词：
Limit theorems; Hermite variations; multiple stochastic integrals; Malliavin calculus; weak convergence; CENTRAL LIMIT-THEOREMS; POWER VARIATIONS; APPROXIMATION; FUNCTIONALS; CONVERGENCE;
D O I：
10.1142/S0219493711500213
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet W-alpha,W-beta with Hurst parameter (alpha, beta) is an element of (0, 1)(2). When 0 < alpha <= 1 - 1/2q or 0 < beta <= 1 - 1/2q a central limit theorem holds for the renormalized Hermite variations of order q >= 2, while for 1 - 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).
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页数：21
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