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Bounded on axes of solutions of linear nonhomogeneous systems of itô's differential equations


the question of existence of unique bounded solution at bounded additive change of , which is stochastic bounded measure, is investigated for the linear system of Itô ordinary differential equations with integrally bounded (on the average) coefficients; it is showed, that if the class of these changes is enough wide (contains absolutely continuous measures with summable density), then existence of bounded solution is possible only in case of uniform exponential stability, i. e. very fast stabilization of solution of homogeneous system; this statement is the direct corollary of the strong events flow irreversibility which is necessary for realization of Wiener measure .


Wiener process; linear equation Itô; problem about the bounded solution; Bohl-Perron's theorem; uniformly exponentially stability

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