Representations of mild solutions of time-varying linear stochastic equations and the exponential stability of periodic systems

V. M. Ungureanu, Constantin Brancusi University, Bul Republicii, nr. 1, Targu-Jiu, jud. Gorj, 1400, Romania

E. J. Qualitative Theory of Diff. Equ., No. 4. (2004), pp. 1-22.

Communicated by Z. Artstein. Appeared on 2004-02-02

Abstract: The main object of this paper is to give a representation of the covariance operator associated to the mild solutions of time-varying,linear, stochastic equations in Hilbert spaces. We use this representation to obtain a characterization of the uniform exponential stability of linear stochastic equations with periodic coefficients.

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