Informatics and Applications
2015, Volume 9, Issue 2, pp 23-29
MODELING OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH COMPLEX TRANSCENDENTAL NONLINEARITIES
- I. N. Sinitsyn
- V. I. Sinitsyn
- E. R. Korepanov
Abstract
Development of methods for analytical and statistical modeling for discrete and continuous stochastic
systems (StS) with Wiener and Poisson noises and with complex transcendental nonlinearities (CTN) is given.
Typical representation of scalar and vector CTN is considered. Equations for the normal approximation method
(NAM) and the method of statistical linearization (MSL) are deduced. Also, NAM and MSL for StS with CTN
algorithms are given. Test examples are presented. Some generalizations are given.
[+] References (14)
- 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
analiticheskogo modelirovaniya 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. 2015.
Modelirovanie normal’nykh protsessov v stokhasticheskikh
sistemakh so slozhnymi irratsional’nymi nelineynostyami
[Modeling of normal processes in stochastic systems
with complex irrational nonlinearities]. Informatika
i ee Primeneniya — Inform. Appl. 9(1):2–8.
- Sinitsyn, I.N., V. I. Sinitsyn, I. V. Sergeev, E.R. Korepanov,
V. V. Belousov, and V. S. Shorgin. 2015. Matematicheskoe
obespechenie modelirovaniya normal’nykh
protsessov v stokhasticheskikh sistemakh so slozhnymi irratsional’nymi
nelineynostyami [Mathematical software
for modeling of normal processes in stochsatic systems
with complex irrational nonlinearities]. Sistemy i Sredstva
Informatiki — Systems and Means of Informatics 25(2):3–
19.
- Popov, B. A., and G. S. Tesler. 1984. Vychislenie funktsiy na
EVM: Spravochnik [Computing of functions:Handbook].
Kiev: Naukova Dumka. 599 ð.
- Kudryavtsev, L.D., and E.D. Solomentsev. 1984. Transtsepdentnaya
funktsiya [Transcendental function]. Matematicheskaya
entsiklopediya [Mathematical encyclopedia].
Ed. I.M. Vinogradov. Moscow: Sovetskaya Entsiklopediya.
425.
- 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.
- Abramovich,M., and I. Stigan, eds. 1979. Spravochnik po
spetsial’nym funktsiyam [Handbook on special functions].
Moscow: Nauka. 832 p.
- Pugachev, V. S., and I.N. Sinitsyn. 1987. Stochastic differential
systems. Analysis and filtering. Chichester, New
York, NY: Jonh Wiley. 549 p.
- Pugachev, V. S., and I.N. Sinitsyn. 2001. Stochastic systems.
Theory and applications. Singapore: Worls Scientific.
908 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. 2012. Matematicheskoe obespechenie
dlya analiza nelineynykh mnogokanal’nykh krugovykh
stokhasticheskikh sistem, osnovannoe na parametrizatsii
raspredeleniy [Mathematical software for analysis of nonlinear
multichannel circular stochastic systems based on
parametrization of distributions]. Informatika i ee Primeneniya
— Inform. Appl. 6(1):12–18.
- Sinitsyn, I.N., E.R. Korepanov, V. V. Belousov, and
T.D. Konashenkova. 2012. Razvitie matematicheskogo
obespecheniya dlya analiza nelineynykh mnogokanal’-
nykh krugovykh stokhasticheskikh sistem [Development
of mathematical software for analysis of nonlinear multichannel
circular stochastic systems]. Sistemy i Sredstva
Informatiki —Systems andMeans of Informatics 22(1):29–
40.
- 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.
[+] About this article
Title
MODELING OF NORMAL PROCESSES IN STOCHASTIC SYSTEMS WITH COMPLEX TRANSCENDENTAL NONLINEARITIES
Journal
Informatics and Applications
2015, Volume 9, Issue 2, pp 23-29
Cover Date
2015-02-30
DOI
10.14357/19922264150203
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
analytical and statistical modeling; complex transcendental nonlinearities (CTN); Hermite polynomials;
method of statistical linearization (MSL); normal approximationmethod (NAM); stochastic systems (StS)
Authors
I. N. Sinitsyn  , V. I. Sinitsyn , and E. R. Korepanov
Author Affiliations
Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian
Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian Federation
|