Stability and convergence of large-scale stochastic approximation procedures

Abstract

In practice, knowledge about input-output systems from various scientific fields such as engineering, biology and the social sciences 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. Convergence and stability results of the solution of continuous time approximation procedures are developed utilizing comparison principles in the context of vector Lyapunov-like functions. In particular, by considering continuous time approximation procedures as large-scale procedures, similar results are obtained using the decomposition-aggregation principle.