Electronic Journal of Qualitative Theory of Differential Equations (Feb 2004)
Representations of mild solutions of time-varying linear stochastic equations and the exponential stability of periodic systems
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.