  In this paper we study the problem of model reduction by moment matching for
stochastic systems. We characterize the mathematical object which generalizes
the notion of moment to stochastic differential equations and we find a class
of models which achieve moment matching. However, differently from the
deterministic case, these reduced-order models cannot be considered "simpler"
because of the high computational cost paid to determine the moment. To
overcome this difficulty, we relax the moment matching problem in two different
ways and we present two classes of reduced-order models which, approximately
matching the stochastic moment, are computationally tractable.
