New results on uniform convergence in probability for the most general classes of wavelet expansions of stationary Gaussian random processes are given.

New results on uniform convergence in probability for expansions of Gaussian random processes using compactly supported wavelets are given. The main result is valid for general classes of non stationary processes. An application of the obtained results to stationary processes is also presented. It is shown that the convergence rate of the expansions is exponential.

The paper characterizes uniform convergence rate for general classes of wavelet expansions of stationary Gaussian random processes. The convergence in probability is considered.

In the paper we present conditions for uniform convergence in probability on [0, T ] of wavelet expansions of random process X = {X(t), t ∈ R}, with E X(t) = 0, E |X(t)| 2 < ∞. We obtain convergence rate of wavelet representation for random processes in the space C(0, T ) as well.

The paper investigates uniform convergence of wavelet expansions of Gaussian random processes. The convergence is obtained under simple general conditions on processes and wavelets which can be easily verified. Applications of the developed technique are shown for several classes of stochastic processes. In particular, the main theorem is adjusted to the fractional Brownian motion case. New results on the rate of convergence of the wavelet expansions in the space C([0, T ]) are also presented.