Optimization of functionals under uncertainties for Ito-Skorokhod stochastic differential equations in Hilbert spaces
DOI:
https://doi.org/10.17721/1812-5409.2018/3.9Abstract
In the article for the stochastic differential equations of Ito-Skorokhod, problems of optimization of functionals under conditions of uncertainty in Hilbert spaces are investigated. Purpose of the article is to investigate some properties of stochastic differential equations in Hilbert spaces. These objects arise in diverse areas of applied mathematics as models for various natural phenomena, in particular, the evolution of complex systems with infinitely many degrees of freedom. For instance, one may think of the liquid fuel motion in the tank of a spacecraft. Spacecraft constructors should take into account this motion, for it influences heavily the path of a spacecraft. Also, optimization of the motion is an issue of principal importance. It is not trivial to carry over the results concerning stochastic differential equations in finite-dimensional spaces to the infinite dimensional case. We give some statements, in which the existence, uniqueness is proved and the explicit form ?-optimal controls for such equations is constructed, in particular, ?-optimal control is found as a linear inverse relationship.
Key words: stochastic differential equation, space of guillotine, optimization of functionals under uncertainty.
Pages of the article in the issue: 65 - 70
Language of the article: Ukrainian
References
SKOROKHOD A. (1987) Asymptotic methods of the theory of stochastic differential equations. – Кyiv: Naukovа dumka.
NAKONECHNYI O., VERES M., STASHCHUK M. (2011) Guaranteed estimates of solutions of linear equations in a Hilbert space with random parameters // Journal of Computational and Applied Mathematics.
DA PRATO G., ZABCZYK J. (2014) Stochastic equations in infinite dimensions, Cambridge University Press.
KOPACHEVSKY, N. (2001) Complete second order linear differential equations in a Hilbert space and hydrodynamics applications. Intern. Conf. Differential Equations and Related Topics, dedicated to the Centenary Anniversary of I.G. Petrovsky, Russia, Moscow, May 22-27, 2001, Book of Abstracts. pp. 207-208.
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