Stochastic uniform observability of linear differential equations with multiplicative noise |
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Authors: | Viorica Mariela Ungureanu |
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Affiliation: | Department of Mathematics, “Constantin Brancusi” University, Tg. Jiu, B-dul Republicii, Nr. 1, jud. Gorj, Romania |
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Abstract: | The aim of this paper is to give a deterministic characterization of the uniform observability property of linear differential equations with multiplicative white noise in infinite dimensions. We also investigate the properties of a class of perturbed evolution operators and we used these properties to give a new representation of the covariance operators associated to the mild solutions of the investigated stochastic differential equations. The obtained results play an important role in obtaining necessary and sufficient conditions for the stochastic uniform observability property. |
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Keywords: | Stochastic differential equations Perturbed evolution operators Covariance operators Stochastic uniform observability Hilbert-Schmidt spaces |
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