Systems and Means of Informatics
2015, Volume 25, Issue 2, pp 3-19
MATHEMATICAL SOFTWARE FOR NORMAL PROCESSES MODELING IN STOCHASTIC SYSTEMS WITH COMPLEX IRRATIONAL NONLINEARITIES
- I. N. Sinitsyn
- V. I. Sinitsyn
- I. V. Sergeev
- E. R. Korepanov
- V. V. Belousov
- V. S. Shorgin
Abstract
Mathematical software for normal stochastic processes (StP) analytical
and statistical modeling in differential and difference (discrete) stochastic systems
(StS) on manifolds with complex irrational nonlinearities (CIRN) of scalar and
vector argument is considered. Typical CIRN and its discrepancy expansions
are presented. Equations for the normal approximation method (NAM) and the
statistical linearization method (SLM) for normal StP analytical modeling are
given. Typical NAM(SLM) integrals and software "StS-CIRN. Analysis" based
on cylindrical functions are discussed. Test examples are given.
[+] References (11)
- Pugachev, V. S., and I. N. Sinitsyn. 1987. Stochastic differential systems. Analysis
and filtering. Chichester, NY: Jonh Wiley. 549 p.
- Pugachev, V. S., and I. N. Sinitsyn. 2001. Stochastic systems. Theory and applications.
Singapore:World Scientific. 908 p.
- Sinitsyn, I. N. 2009. Kanonicheskie predstavleniya sluchaynykh funktsiy i ikh primenenie v zadachakh komp'yuternoy podderzhki nauchnykh issledovaniy [Canonical
expansions of random functions and their application to scientific computer-aided
support]. Moscow: TORUS PRESS. 768 p.
- Sinitsyn, I. N., and V. I. Sinitsyn. 2013. Lektsii po normal'noy i ellipsoidal'noy
approksimatsii raspredeleniy v stokhasticheskikh sistemakh [Lectures on normal and
ellipsoidal approximation of distributions in stochastic systems]. Moscow: TORUS
PRESS. 488 p.
- Sinitsyn, I. N. 2013. Parametricheskoe statisticheskoe i analiticheskoe modelirovanie
raspredeleniy v nelineynykh stokhasticheskikh sistemakh na mnogoobraziyakh [Parametric statistical and analytical modeling of distributions in stochastic systems on
manifolds]. Informatika i ee Primeneniya - Inform. Appl. 7(2):4-16.
- Sinitsyn, I. N., and V. I. Sinitsyn. 2014. Analiticheskoe modelirovanie normal'nykh
protsessov v stokhasticheskikh sistemakh so slozhnymi nelineynostyami [Analytical
modeling of normal processes in stochastic systems with complex nonlinearities].
Informatika i ee Primeneniya - Inform. Appl. 8(3):2-4.
- Sinitsyn, I. N., V. I. Sinitsyn, I.V. Sergeev, V.V. Belousov, and V. S. Shorgin.
2014. Matematicheskoe obespechenie analiticheskogomodelirovaniya stokhasticheskikh
sistem so slozhnymi nelineynostyami [Mathematical software for analytical modeling
of stochastic systems with complex nonlinearities]. Sistemy i Sredstva Informatiki -
Systems and Means of Informatics 24(3):4-29.
- Sinitsyn, I. N., V. I. Sinitsyn, and E.R. Korepanov. 2014. Modelirovanie normal'nykh
protsessov v stokhasticheskikh sistemakh so slozhnymi irratsional'nymi nelineynostyami
[Modeling of processes in stochastic systems with complex irrational nonlinearities].
Informatika i ee Primeneniya - Inform. Appl. 9(1):2-8.
- Gradshteyn, I. S., and I.M. Ryzhik. 1963. Tablitsy integralov, summ, ryadov i proizvedeniy [Tables of integrals, sums, series, and products]. Moscow: GIFML. 1100 p.
- Popov, B.A., and G. S. Tesler. 1984. Vychislenie funktsiy na EVM. Spravochnik
[Computing of functions]. Kiev: Naukova Dumka. 599 p.
- Sinitsyn, I. N., V. I. Sinitsyn, I.V. Sergeev, E.R. Korepanov, V.V. Belousov,
and V. S. Shorgin. 2015. Rukovodstvo pol'zovatelya biblioteki "StS-ANALYSIS"
(versiya 1.0) ["StS-ANALYSIS" (version 1.0) Manual]. Ed. I. N. Sinitsyn. Moscow:
IPI RAN. Preprint. 47 p.
[+] About this article
Title
MATHEMATICAL SOFTWARE FOR NORMAL PROCESSES MODELING IN STOCHASTIC SYSTEMS WITH COMPLEX IRRATIONAL NONLINEARITIES
Journal
Systems and Means of Informatics
Volume 25, Issue 2, pp 3-19
Cover Date
2015-01-30
DOI
10.14357/08696527150201
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
analytical and statistical modeling; complex irrational nonlinearity (CIRN); cylindrical functions; Hermite polynomials; module "StS-CIRN.Analysis;" normal approximation method (NAM); statistical linearizatio nmethod
(SLM)
Authors
I.N. Sinitsyn , V. I. Sinitsyn ,
I. V. Sergeev , E. R. Korepanov ,
V. V. Belousov , and V. S. Shorgin
Author Affiliations
Institute of Informatics Problems, Federal Research Center "Computer Science
and Control", Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
|