Stationary solutions for linear systems with additive noise

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Abstract
The eq. is considered, with (z t being a stationary process in and The existence of solutions (*) to such that (x t , z t ) is stationary is investigated. Strong and weak stationary solutions are considered. it is shown that if weak stationary solutions exist so do strong stationary solutions, the necessary and sufficient condition for existence being the a.s. Caesaro convergence as to a rendom process L(u), such that L(u) is a.s. a characteristic function.

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