Abstract
In this paper we study a general concept of nonuniform exponential dichotomy in mean square for stochastic skew-evolution semiflows in Hilbert spaces. We obtain a variant for the stochastic case of some well-known results, of the deterministic case, due to R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space, SIAM J. Math. Anal., 3(1972), 428–445. Our approach is based on the extension of some techniques used in the deterministic case for the study of asymptotic behavior of skew-evolution semiflows in Banach spaces.
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This work was partially supported by the strategic grant POSDRU/21/1.5/G/13798, inside POSDRU Romania 2007-2013, co-financed by the European Social Fund — Investing in People and by Exploratory Research Grant PN II ID 1080/2009 of the Romanian Ministry of Education, Reserch and Inovation.
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Stoica, D., Megan, M. On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces. Czech Math J 62, 879–887 (2012). https://doi.org/10.1007/s10587-012-0071-0
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DOI: https://doi.org/10.1007/s10587-012-0071-0