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On integral separation of bounded linear random differential equations

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  • Our aim in this paper is to investigate the openness and denseness for the set of integrally separated systems in the space of bounded linear random differential equations equipped with the $L^{\infty}$-metric. We show that in the general case, the set of integrally separated systems is open and dense. An exception is the case when the base space is isomorphic to the ergodic rotation flow of the unit circle, in which the set of integrally separated systems is open but not dense.
    Mathematics Subject Classification: Primary: 37A20, 37A10, 37Hxx; Secondary: 34D08.


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