Abstract
In this thesis we give a sufficient condition for the almost sure convergence of weighted sums of T_n=a_{n1}*X_1+a_{n2}*X_2+...+a_{nk}*X_k+..., where {X_k,k=1,2,...} be a sequence of φ-subgaussian random variables. Further-more, an application to the Fourier analysis is given. Moreprecisely, let {X_n,n=1,2,...} be a sequence of φ-subgauss-ian random variables and {D_n,n=1,2,...} be an arbitrarysequence of random variables. We consider the convergenceof the series a_1*X_1*cos(t+D_1)+...+a_n*X_n*cos(nt+D_n)+...,0≦t≦2π to a stochastic process f(t),0≦t≦2π.