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On convergence of general wavelet decompositions of nonstationary stochastic processes


 
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1. Title Title of document On convergence of general wavelet decompositions of nonstationary stochastic processes
 
2. Creator Author's name, affiliation, country Yuriy Kozachenko; Kyiv University; Ukraine
 
2. Creator Author's name, affiliation, country Andriy Olenko; La Trobe University; Australia
 
2. Creator Author's name, affiliation, country Olga Polosmak; Kyiv University; Ukraine
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Convergence in probability; Uniform convergence; Convergence rate; Gaussian process; Fractional Brownian motion; Wavelets
 
3. Subject Subject classification 60G10; 60G15; 42C40
 
4. Description 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) La Trobe University Research Grant "Stochastic Approximation in Finance and Signal Processing."
 
7. Date (YYYY-MM-DD) 2013-07-25
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2234
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2234
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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