descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 16 Oct 2018Publisher:Kyiv Politechnic InstituteJournal:System research and information technologies, volume 0, pages 80-90 (issn: 1681-6048, eissn: 2308-8893,

Authors: Yasynskyy, Volodymyr K.; Yurchenko, Igor V.;

doi: 10.20535/srit.2308-8893.2018.3.07

On existence and stabilization of the strong solution of the autonomous stochastic partial differential Ito-Skorokhod equation with random parameters

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Abstract

This paper considers the asymptotic behavior of the strong solution of the linear partial stochastic differential Ito–Skorokhod equation in the corresponding space with random parameters. An existence of the strong solution is proved and sufficient conditions for the asymptotic stability and the mean square instability of a strong solution of a similar equation are obtained. The stochastic model of complex systems, which is proposed in this paper, is an attempt to take into consideration the full extent of randomness in the studying of real processes, which are described by differential equations in partial derivatives, on the right side of which a diffuse perturbations of the Brownian process type and random perturbations of other types are taken into consideration.

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Keywords

Cauchy problem, mean square stability, asymptotic stability, random perturbations, QA75.5-76.95, stochastic partial differential equation, existence of the solution, задача Коші; стохастичне диференціальне рівняння в частинних похідних; існування розв’язку; випадкові збурення, Electronic computers. Computer science, задача Коши; стохастическое дифференциальное уравнение в частных производных; существование решения; случайные возмущения, Cauchy problem; stochastic partial differential equation; existence of the solution; random perturbations

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