Systems and Means of Informatics
2024, Volume 34, Issue 2, pp 21-39
NON STATIONARY STOCHASTIC PROCESS MODELING BY CANONICAL EXPANSION AND WAVELET NEUTRAL NETWORK
- I. N. Sinitsyn
- V. I. Sinitsyn
- E. R. Korepanov
- T. D. Konashenkova
Abstract
For scalar stochastic processes (StP) at finite time intervals and their canonical expansions (CE), a technology based on wavelet neural networks (WNN) is constructed. For WNN learning, the method of steepest descent was used. The three-layer WNN architecture is presented. The activation functions of the latent layer are based on chosen wavelet basis with general compact carrier.
For StP covariance function, a special WNN algorithm of CE construction is developed. The covariance function CE corresponds to CE StP in the form of linear combination of wavelet basis with zero mathematical expectations and variances defined by the suggested algorithm. A numerical example illustrates CE WNN preference with wavelet CE.
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[+] About this article
Title
NON STATIONARY STOCHASTIC PROCESS MODELING BY CANONICAL EXPANSION AND WAVELET NEUTRAL NETWORK
Journal
Systems and Means of Informatics
Volume 34, Issue 2, pp 21-39
Cover Date
2024-05-20
DOI
10.14357/08696527240202
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
canonical expansion; covariance function; modeling; stochastic process; wavelet; wavelet neural network
Authors
I. N. Sinitsyn  , V. I. Sinitsyn , E. R. Korepanov , and T. D. Konashenkova
Author Affiliations
Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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