  In this paper, we study connections between the classical model-based
approach to nonlinear system theory, where systems are represented by
equations, and the nonlinear behavioral approach, where systems are defined as
sets of trajectories. In particular, we focus on equivalent representations of
the systems in the two frameworks for the problem of simulating a future
nonlinear system trajectory starting from a given set of noisy data. The goal
also includes extending some existing results from the deterministic to the
stochastic setting.
