Almost sure central limit theorems on the Wiener space

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Bercu, Bernard²  Nourdin, Ivan¹  Taqqu, Murad S.³ 

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

[2] Univ Bordeaux 1, Inst Math Bordeaux, F-33405 Talence, France

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

关键词: Almost sure limit theorem;    Multiple stochastic integrals;    Fractional Brownian motion;    Hermite power variation;   

DOI  :  10.1016/j.spa.2010.05.004

来源: Elsevier

【 摘 要 】

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law to a normal distribution. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free