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On convergence of general wavelet decompositions of nonstationary stochastic processes. (English) Zbl 1291.60073

Authors’ abstract: 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.

MSC:

60G15 Gaussian processes
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
60G22 Fractional processes, including fractional Brownian motion
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