An application of -subgaussian technique to Fourier analysis

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.