Modeling algorithms for vector stochastic process by canonical expansions based on multilayer wavelet neural network

The paper is devoted to modeling methods and algorithms for vector stochastic process (StP) based on multilayer canonical expansions (CE) of wavelet neural network (WNN). Stochastic process is defined on a fixed time interval. Canonical expansion for matrix covariance functions construction is considered as approximation problem for elements of covariance functions by quadratic forms of basic wavelet with compact carriers. For its solution, multilayer architecture of WNN is developed. Training with teacher is realized by inverse error extension method. The CE of coordinate functions are taken in linear combination of basic wavelet functions with weighting coefficients whose optimal values are defined during WNN functioning. Special attention is paid to two-dimensional typical nonstationary StP. Advantages of CE of WNN algorithms are discussed.