Central and Non-central Limit Theorems in a Free Probability Setting

被引：12

作者：

Nourdin, Ivan ^{[1
,2
]}

Taqqu, Murad S. ^{[3
]}

机构：

[1] Univ Lorraine, Inst Math Elie Cartan, Fac Sci & Tech, F-54506 Vandoeuvre Les Nancy, France

[2] Fdn Sci Math Paris, IHP, F-75231 Paris 05, France

[3] Boston Univ, Dept Math, Boston, MA 02215 USA

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2014年 / 27卷 / 01期

关键词：

Central limit theorem; Non-central limit theorem; Convergence in distribution; Fractional Brownian motion; Free Brownian motion; Free probability; Rosenblatt process; Wigner integral; BROWNIAN-MOTION; CONVERGENCE; FUNCTIONALS;

D O I：

10.1007/s10959-012-0443-2

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：

Long-range dependence in time series may yield non-central limit theorems. We show that there are analogous time series in free probability with limits represented by multiple Wigner integrals, where Hermite processes are replaced by non-commutative Tchebycheff processes. This includes the non-commutative fractional Brownian motion and the non-commutative Rosenblatt process.

引用

页码：220 / 248

页数：29

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