Informatics and Applications
2023, Volume 17, Issue 1, pp 2-10
ANALYTICAL MODELING OF DISTRIBUTIONS WITH INVARIANT MEASURE IN STOCHASTIC SYSTEMS WITH UNSOLVED DERIVATIVES
Abstract
Exact and approximate analytical modeling methods for stochastic processes with invariant measure in Gaussian and non-Gaussian stochastic systems with unsolved derivatives are considered. The methods are based on the linear regression approximation of nonlinear functions with unsolved derivatives and reduction to stochastic Ito differential equations. Two exact methods for analytical modeling of one- and multidimensional distributions with invariant measure are described. Special attention is paid to normal approximation and parametrization methods. A test example for Duffing equation nonlinear in second derivative is given. The stationary and nonstationary regimes and asymptotic stability are investigated. The method of normal approximation for one- and two-dimensional distributions is accurate enough for engineering applications. Some generalizations concerning numerical analytical modeling are considered.
[+] References (12)
- Sinitsyn, I. N. 2012. Analiticheskoe modelirovanie raspredeleniy s invariantnoy meroy v stokhasticheskikh sistemakh s avtokorrelirovannymi shumami [Analytical modeling of distributions with invariant measures in stochastic systems with autocorrelated noises]. Informati- ka i ee Primeneniya - Inform. Appl. 6(4):4-8.
- Soize, C. 1994. The Fokker-Plank equation for stochastic dynamical systems and its explicit steady state solutions. Singapore: World Scientific. 321 p.
- Sinitsyn, I. N. 2013. Analiticheskoe modelirovanie raspredeleniy s invariantnoy meroy v stokhasticheskikh sistemakh s razryvnymi kharakteristikami [Analytical modeling of distributions with invariant measure in stochastic systems with discontinuous characteristics]. Informatika i ee Primeneniya - Inform. Appl. 7(1):3-11.
- Sinitsyn, I. N. 2012. Razvitie metodov analiticheskogo modelirovaniya raspredeleniy s invariantnoy meroy v stokhasticheskikh sistemakh [Development of analytical modeling methods for distributions with invariant measure in stochastic systems]. Sovremennye problemy prikladnoy matematiki, informatiki, avtomatizatsii, upravleniya:
Mat-ly Mezhdunar. seminara [Modern Problems of Applied Mathematics Informatics, Automation and Control: Seminar (International) Proceedings]. Sevastopol': SevNTU. 24-35.
- Sinitsyn, I. N. 2017. Analiticheskoe modelirovanie shirokopolosnykh protsessov v stokhasticheskikh sistemakh, ne razreshennykh otnositel'no proizvodnykh
[Analytical modeling of wide band processes in stochastic systems with unsolved derivatives]. Informatika i ee Primeneniya - Inform. Appl. 11(1):3-10.
- Sinitsyn, I. N. 2017. Parametricheskoe analiticheskoe modelirovanie protsessov v stokhasticheskikh sistemakh, ne razreshennykh otnositel'no proizvodnykh
[Parametric analytical modeling of processes in stochastic systems that are not allowed with respect to derivatives]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 27(1): 21-45.
- Sinitsyn, I. N. 2021. Analytical modeling and estimation of normal processes defined by stochastic differential equations with unsolved derivates. J. Mathematics Statistics Research 3(1):139. 7 p.
- Sinitsyn, I. N. 2022. Analiticheskoe modelirovanie i otsenivanie nestatsionarnykh normal'nykh protsessov v stokhasticheskikh sistemakh, ne razreshennykh otnositel'no proizvodnykh
[Anatlytical modeling and estmation of nonstationary normal processes with unsolved derivatives]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 32(2):58-71.
- Sinitsyn, I. N. 2022. Normalizatsiya sistem, stokhasticheski ne razreshennykh otnositel'no proizvodnykh
[Normalization of systems with stochastically unsolved derivatives]. Informatika i ee Primeneniya - Inform. Appl. 16(1):32-38.
- Pugachev, V.S., and I. N. Sinitsyn. 2000, 2004. Teoriya stokhasticheskikh sistem [Stochastic systems. Theory and applications]. Moscow: Logos. 1000 p.
- Aleksandrovskaya, L. N., I. Z. Aronov, V.I. Kruglov, et al. 2008. Bezopasnost' i nadezhnost' tekhnicheskikh sistem [Security and safety of technical systems]. Moscow: Universitetskaya kniga, Logos. 348 p.
- Sinitsyn, I. N., and A. S. Shalamov. 2019. Lektsiipo teorii sistem integrirovannoy logisticheskoy podderzhki [Lectures on theory of integrated logistic support systems]. 2nd ed. Moscow: TORUS PRESS. 1072 p.
[+] About this article
Title
ANALYTICAL MODELING OF DISTRIBUTIONS WITH INVARIANT MEASURE IN STOCHASTIC SYSTEMS WITH UNSOLVED DERIVATIVES
Journal
Informatics and Applications
2023, Volume 17, Issue 1, pp 2-10
Cover Date
2023-04-10
DOI
10.14357/19922264230101
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
analytical modeling; distribution parametrization; distribution with invariant measure; stochastic system; stochastic system with unsolved derivatives; stochastic process
Authors
I. N. Sinitsyn  , 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
Moscow State Aviation Institute (National Research University), 4 Volokolamskoe Shosse, Moscow 125933, Russian Federation
|