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

Authors

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2018.3.07

Keywords:

Cauchy problem, stochastic partial differential equation, existence of the solution, random perturbations

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.

Author Biographies

Volodymyr K. Yasynskyy, Yurij Fedkovych Chernivtsi National University, Chernivtsi

Volodymyr Kyryllovych Yasynskyy,

doctor of ph.-math.sciences, a professor at the department of system analysis and actuarial and financial mathematics of Yurij Fedkovych Chernivtsi National University, Chernivtsi, Ukraine.

Research interests: stochastic differential equations.

Igor V. Yurchenko, Yurij Fedkovych Chernivtsi National University, Chernivtsi

Igor Valeryjovych Yurchenko,

candidate of ph.-math. sciences, docent at the department of mathematical modelling of faculty of mathematics and informatics of Yurij Fedkovych Chernivtsi National University, Chernivtsi, Ukraine.

Research interests: stochastic differential equations.

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Published

2018-10-16

Issue

No. 3 (2018)

Section

Mathematical methods, models, problems and technologies for complex systems research

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