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.
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页码：220 / 248
页数：29
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