In practice knowledge about input-output systems from various scientific fields such as engineering, biology, and social science is limited to output data. In this work we consider the continuous version of the discrete approximation procedure relative to such a system whose outcome is known at a time and a point. The stochastic approximation procedure is described by a Ito-type stochastic differential system. We will consider such a system in both the absence and presence of the effects of random structural changes in the system. Convergence and stability results of the solution of these systems are developed utilizing comparison principles in the context of vector Lyapunov-like functions. In particular, by considering continuous time approximation procedures similar results are obtained using the decomposition-aggregation principle. As a by-product of the study, the effects of random structural perturbations are also analyzed. The usefulness of the presented convergence results is exhibited in an application from the field of Economics.
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