Czechoslovak Mathematical Journal, Vol. 62, No. 4, pp. 879-887, 2012

On nonuniform dichotomy for stochastic skew-evolution semiflows in Hilbert spaces

Diana Stoica, Mihail Megan

Diana Stoica, Politehnica University of Timişoara, Engineering Faculty of Hunedoara, Revoluţiei 5, 331128, Hunedoara, Romania, e-mail: diana.stoica@fih.upt.ro; Mihail Megan, Academy of Romanian Scientists, Independenţei 54, Bucharest, 050094, West University of Timişoara, Department of Mathematics, Bd. V. Parvan 4, 300223, Timişoara, Romania, e-mail: megan@math.uvt.ro

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.

Keywords: stochastic skew-evolution semiflow, nonuniform exponential dichotomy in mean square

Classification (MSC 2010): 37L55, 60H25, 93E15


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