ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Modeling and Analysis of Linear Invariant Stochastic Systems


Tatyana Averina

Institute of Computational Mathematics and Mathematical Geophysics SB RAS;
Novosibirsk State University

Elena Karachanskaya

Far Eastern State Transport University,
Pacific National University

Konstantin Rybakov

Moscow Aviation Institute (National Research University)


The main aim of this paper is to test the numerical methods for stochastic differential equations with solutions on a given smooth manifold. Cylindrical surfaces of the second order are selected as manifolds examples for the three-dimensional space (two-dimensional phase space): elliptic, hyperbolic, and parabolic cylinders. We construct classes of stochastic differential equations with solutions on these surfaces and consider linear equations with multiplicative noise. The numerical methods accuracy is estimated by the statistical modeling as mean distance between simulated solutions and the given smooth manifold. These results are compared with a theoretical accuracy of the numerical methods (in the sense of strong convergence).



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