Abstract
In this paper the almost sure practical stability with respect to some given continuous time-varying sets of the state space for Ito stochastic differential systems (SDS) is studied by means of Lyapunov-like functions and Comparison Method The comparative criteria of a.s. practical stability, a.s. practical and uniform stability, a.s. practical unstability as well as a.s. practical asymptotic stability are established. Using these criteria, with respect to time-varying sets, we can reduce the judgement of the a.s. practical stability for a general n-dimensional its SDS to that for a concomitant deterministic 1-dimensional ordinary differential auxiliary system (ODAS)
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