Convergence of Fourier-wavelet models for Gaussian random processes
- Kurbanmuradov, Orazgeldy
- Sabelfeld, Karl
2010 Mathematics Subject Classification
- 65C05 65C20 60G15
2008 Physics and Astronomy Classification Scheme
- Fourier-Wavelet model, stationary Gaussian random process, Meyer's wavelets, Nikolskiui-Besov space, convergence in probability, convergence in mean square
Mean square convergence and convergence in probability of Fourier-Wavelet Models (FWM) of stationary Gaussian Random processes in the metric of Banach space of continuously differentiable functions and in Sobolev space are studied. Sufficient conditions for the convergence formulated in the frame of spectral functions are given. It is shown that the given rates of convergence of FWM in the mean square obtained in the Nikolskiui-Besov classes cannot be improved.