COMPARISON OF DIFFERENT WAVELET BASES IN THE CASE OF WAVELETS EXPANSIONS OF RANDOM PROCESSES
In the paper wavelets expansions of random processes are studied. The matter is that although it is enough information for wavelets expansions of deterministic functions, for random processes such theory is weak and it should be developed. 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 wavelet bases. So, conditions of uniform convergence for Battle Lemarie wavelets and Meyer wavelets expansions of Gaussian random processes are presented. Another useful in various computational applications thing is the rate of convergence, especially if we are interested in the optimality of the stochastic approximation or the simulations. An explicit estimate of the rate of uniform convergence for Battle Lemarie wavelets and Meyer wavelets expansions of Gaussian random processes is obtained and compared.