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

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

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Applying spectral form of mathematical description for representation of iterated stochastic integrals

Author(s):

Konstantin Rybakov

Moscow Aviation Institute (National Research University)

rkoffice@mail.ru

Abstract:

The article describes some aspects for applying the spectral form of mathematical description, which is used for the control systems analysis and synthesis, for the representation of iterated stochastic second multiplicity integrals with respect to the numerical solution of stochastic differential equations. It is proposed to use the spectral characteristics of the integration operator (two-dimensional nonstationary transfer functions of the integrator) defined by different orthonormal function systems: Legendre polynomials, cosines, Walsh and Haar functions, as well as the trigonometric Fourier basis.

Keywords

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