The conditional central limit theorem in Hilbert spaces

被引：33

作者：

Dedecker, J ^{[1
]}

Merlevède, F ^{[1
]}

机构：

[1] Univ Paris 06, LSTA, F-75013 Paris, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2003年 / 108卷 / 02期

关键词：

Hilbert space; central limit theorem; weak invariance principle; strictly stationary process; stable convergence; strong mixing; mixingale; linear processes;

D O I：

10.1016/j.spa.2003.07.004

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：

in this paper, we give necessary and sufficient conditions for a stationary sequence of random variables with values in a separable Hilbert space to satisfy the conditional central limit theorem introduced in Dedecker and Merlevede (Ann. Probab. 30 (2002) 1044-1081). As a consequence, this theorem implies stable convergence of the normalized partial sums to a mixture of normal distributions. We also establish the functional version of this theorem. Next, we show that these conditions are satisfied for a large class of weakly dependent sequences, including strongly mixing sequences as well as mixingales. Finally, we present an application to linear processes generated by some stationary sequences of H-valued random variables. (C) 2003 Elsevier B.V. All rights reserved.

引用

页码：229 / 262

页数：34

共 38 条

[1] MIXING AND STABILITY OF LIMIT-THEOREMS [J].