Electronic Journal of Probability

On convergence of general wavelet decompositions of nonstationary stochastic processes

Yuriy Kozachenko, Andriy Olenko, and Olga Polosmak

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 18 (2013), paper no. 69, 21 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465064294

Digital Object Identifier
doi:10.1214/EJP.v18-2234

Mathematical Reviews number (MathSciNet)
MR3084655

Zentralblatt MATH identifier
1291.60073

Subjects
Primary: 60G10: Stationary processes
Secondary: 60G15: Gaussian processes 42C40: Wavelets and other special systems

Keywords
Convergence in probability Uniform convergence Convergence rate Gaussian process Fractional Brownian motion Wavelets

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

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


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