Non-central limit theorem of the weighted power variations of Gaussian processes

被引：0

作者：

Kim, Iltae ^{[1
]}

Park, Hyun Suk ^{[2
]}

Kim, Yoon Tae ^{[2
]}

机构：

[1] Chonnam Natl Univ, Dept Econ, Kwangju 500757, South Korea

[2] Hallym Univ, Dept Stat, Chunchon 200702, Gangwon Do, South Korea

来源：

JOURNAL OF THE KOREAN STATISTICAL SOCIETY | 2014年 / 43卷 / 02期

关键词：

Malliavin calculus; Fractional Brownian motion; Non-central limit theorem; Power variation; Multiple stochastic integral; RESPECT;

D O I：

10.1016/j.jkss.2013.09.001

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：

By using the techniques of the Malliavin calculus, we investigate the asymptotic behavior of the weighted q-variations of continuous Gaussian process of the form B-t = integral(t)(0) K (t, s) dW (s), where W is the standard Brownian motion and K is a square integrable kernel. In particular, in the case of fractional Brownian motion with the Hurst parameter H, the limit can be expressed as the sum of q + 1 Skorohod integrals of the Hermite process with self-similarity q(H - 1) + 1. This result gives the relation between the Skorohod integral and a pathwise Young integral of the Hermite process. (C) 2013 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

引用

页码：215 / 223

页数：9

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