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Modeling of multistructural systems on manifolds for statistical analysis and filtering problems

Annotation

We propose an extension for the stochastic dynamical systems whose trajectories belong to a given manifold. This extension is the stochastic multistructural systems, namely the systems with a variable and random structure. The description for such systems are considered in application to analysis and filtering problems.

Keywords

invariant stochastic system; first integral; numerical method; random process; system with variable structure; system with random structure; stochastic differential equation

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DOI

10.20310/1810-0198-2018-23-122-145-153

UDC

519.217

Pages

145-153

References

1. Kazakov I.E., Artemev V.M., Bukhalev V.A. Analiz sistem sluchaynoy struktury [Analysis of Systems with Random Structure]. Moscow, Fizmatlit Publ., 1993, 272 p. (In Russian). 2. Dubko V.A., Karachanskaya E.V. Spetsial'nye razdely teorii stokhasticheskikh differentsial'nykh uravneniy [Special Chapters of the Theory of Stochastic Differential Equations]. Khabarovsk, Pacific National University, 2013, 91 p. (In Russian). 3. Kolmogorov A.N., Prokhorov Y.V., Shiryaev A.N. Veroyatnostno-statisticheskie metody obnaruzheniya spontanno voznikayushchikh effektov [Probabilistic-statistical methods of detecting spontaneously occurring effects]. Trudy Matematicheskogo instituta im. V.A. Steklova AN SSSR – Proceedings of the Steklov Institute of Mathematics, 1988, vol. 182, no. 5, pp. 4-23. (In Russian). 4. Shiryaev A.N. Stokhasticheskie zadachi o razladke [Stochastic Disorder Problems]. Moscow, Moscow Center for Continuous Mathematical Education, 2016, 392 p. (In Russian). 5. Rybakov K.A. Statisticheskie metody analiza i fil'tratsii v nepreryvnykh stokhasticheskikh sistemakh [Statistical Methods of Analysis and Filtering for Continuous Stochastic Systems]. Moscow, Moscow Aviation Institute, 2017, 176 p. (In Russian). 6. Averina T.A., Karachanskaya E.V., Rybakov K.A. Statistical analysis of diffusion systems with invariants. Rus. J. Numer. Anal. Math. Modelling, 2018, vol. 33, no. 1, pp. 1-13. 7. Averina T.A. Chislennyy analiz sistem upravleniya dinamicheskimi ob"ektami so sluchaynymi izmeneniyami struktury [Numerical analysis of multistructural control systems of dynamic objects]. Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences, 2011, vol. 16, no. 4, pp. 1023-1026. (In Russian). 8. Averina T.A. Postroenie i obosnovanie statisticheskikh algoritmov modelirovaniya resheniya sistem so sluchaynoy strukturoy, zadannoy stokhasticheskimi differentsial'nymi uravneniyami [Construction and justification of statistical algorithms for simulation of switching diffusion, given by stochastic differential equations]. Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki – Tambov University Reports. Series: Natural and Technical Sciences, 2015, vol. 20, no. 5, pp. 986-991. (In Russian).

Received

2018-03-22

Section of issue

Scientific articles

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