ASYMPTOTIC BEHAVIOR OF WEIGHTED QUADRATIC AND CUBIC VARIATIONS OF FRACTIONAL BROWNIAN MOTION

被引：39

作者：

Nourdin, Ivan ^{[1
]}

机构：

[1] Univ Paris 06, Lab Probabilites & Modeles Aleatoires, F-75252 Paris 05, France

来源：

ANNALS OF PROBABILITY | 2008年 / 36卷 / 06期

关键词：

Fractional Brownian motion; Breuer and Major theorem; weighted quadratic variation; weighted cubic variation; exact rate of convergence; Malliavin calculus;

D O I：

10.1214/07-AOP385

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：

The present article is devoted to a fine study of the convergence of renormalized weighted quadratic and cubic variations of a fractional Brownian motion B with Hurst index H. In the quadratic (resp. Cubic) case, when H < 1/4 (resp. H < 1/6). we show by means of Malliavin Calculus that the convergence holds in L(2) toward in explicit limit which only depends on B. This result is somewhat surprising when compared with the celebrated Breuer and Major theorem.

引用

页码：2159 / 2175

页数：17

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