Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions

Abstract

This article is devoted to analysis and optimization problems of stochastic systems based on wavelet canonical expansions. Basic new results: (i) for general Bayes criteria, a method of synthesized methodological support and a software tool for nonstationary normal (Gaussian) linear observable stochastic systems by Haar wavelet canonical expansions are presented; (ii) a method of synthesis of a linear optimal observable system for criterion of the maximal probability that a signal will not exceed a particular value in absolute magnitude is given. Applications: wavelet model building of essentially nonstationary stochastic processes and parameters calibration.