Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions

被引：3

作者：

Sinitsyn, Igor ^{[1
,2
]}

Sinitsyn, Vladimir ^{[1
,2
]}

Korepanov, Eduard ^{[1
]}

Konashenkova, Tatyana ^{[1
]}

机构：

[1] Russian Acad Sci FRC CSC RAS, Fed Res Ctr Comp Sci & Control, Moscow 119333, Russia

[2] Natl Res Univ, Moscow Aviat Inst, Moscow 125993, Russia

来源：

MATHEMATICS | 2022年 / 10卷 / 09期

关键词：

Bayes criterion; Haar wavelets; loss function; mean risk; observable stochastic systems (OStS); stochastic process (StP); wavelet canonical expansion (WLCE); NUMERICAL-SOLUTION; DIFFERENTIAL-EQUATIONS; ORTHONORMAL BASES;

D O I：

10.3390/math10091517

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：14

共 31 条

[1]

Arora S., 2014, International Journal of Computer Applications, V97, P33, DOI 10.5120/17108-7759

[2]

Cattani C., 2004, Proceedings of the Estonian Academy of Sciences, Physics, Mathematics, V53, P45, DOI [10.3176/phys.math.2004.1.04, DOI 10.3176/PHYS.MATH.2004.1.04]

[3] Haar wavelet method for solving lumped and distributed-parameter systems [J].