An application of φ-subgaussian technique to Fourier analysis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Antonini, Rita Giuliano¹  Hu, Tien-Chung²  Kozachenko, Yuriy³  Volodin, Andrei⁴ 

[1] Univ Pisa, Dipartimento Matemat, I-56100 Pisa, Italy

[2] Natl Tsing Hua Univ, Dept Math, Hsinchu 30013, Taiwan

[3] Kyiv Natl Taras Shevchenko Univ, Fac Math & Mech, UA-01033 Kiev, Ukraine

[4] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

关键词: phi-subgaussian random variables;    Convergence in probability;    Convergence almost surely;    Random Fourier series;    Random trigonometric polynomial;   

DOI  :  10.1016/j.jmaa.2013.05.063

来源: Elsevier

【 摘 要 】

We present an application to random Fourier series for phi-subgaussian random variables. In particular, we generalize previously known notions of dependence for random variables by introducing the concept of F-manageable random variables, and consider Fourier series of F-manageable phi-subgaussian random variables. Gaussian series are then a particular case of the series considered in the paper. Conditions for the uniform convergence of such series in probability are established and a rate of convergence is investigated. Moreover, the results are new even for the case of independent random variables. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free