Open Access
2013 On convergence of general wavelet decompositions of nonstationary stochastic processes
Yuriy Kozachenko, Andriy Olenko, Olga Polosmak
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Electron. J. Probab. 18: 1-21 (2013). DOI: 10.1214/EJP.v18-2234


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.


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Yuriy Kozachenko. Andriy Olenko. Olga Polosmak. "On convergence of general wavelet decompositions of nonstationary stochastic processes." Electron. J. Probab. 18 1 - 21, 2013.


Accepted: 25 July 2013; Published: 2013
First available in Project Euclid: 4 June 2016

zbMATH: 1291.60073
MathSciNet: MR3084655
Digital Object Identifier: 10.1214/EJP.v18-2234

Primary: 60G10
Secondary: ‎42C40 , 60G15

Keywords: convergence in probability , convergence rate , fractional Brownian motion , Gaussian process , Uniform convergence , Wavelets

Vol.18 • 2013
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