Electronic Journal of Probability
- Electron. J. Probab.
- Volume 18 (2013), paper no. 69, 21 pp.
On convergence of general wavelet decompositions of nonstationary stochastic processes
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.
Electron. J. Probab., Volume 18 (2013), paper no. 69, 21 pp.
Accepted: 25 July 2013
First available in Project Euclid: 4 June 2016
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Kozachenko, Yuriy; Olenko, Andriy; Polosmak, Olga. On convergence of general wavelet decompositions of nonstationary stochastic processes. Electron. J. Probab. 18 (2013), paper no. 69, 21 pp. doi:10.1214/EJP.v18-2234. https://projecteuclid.org/euclid.ejp/1465064294