Nonstationary stochastic process modeling by canonical expansion and wavelet neutral network

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.