We present an application to random Fourier series for φ-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 φ-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.

An application of φ-subgaussian technique to Fourier analysis

GIULIANO, RITA;
2013

Abstract

We present an application to random Fourier series for φ-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 φ-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.
Giuliano, Rita; Hu, T. C.; Kozachenkoy, ; Volodin, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/212142
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