  In this paper, a simulation-based method for the analysis and design of
abstracted models for a stochastic hybrid system is proposed. The accuracy of a
model is evaluated in terms of its capability to reproduce the system output
for all the realizations of the stochastic input except for a set of (small)
probability epsilon (epsilon-abstraction). This naturally leads to
chance-constrained optimization problems, which are here tackled by means of a
recently developed randomized approach. The main thrust of this paper is that,
by testing how close the model and system outputs are over a finite number N of
input realizations only, conclusions can be drawn about the model capability as
an epsilon-abstraction. The key feature of the proposed method is its high
versatility since it does not require specific assumptions on the system to be
approximated. The only requirement is that of being able to run multiple
simulations of the system behavior for different input realizations.
