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.
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页数：14
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