On Moment Matching for Stochastic Systems

In this article, we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object that generalizes the notion of moment to stochastic differential equations, and find a class of models that 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 present two classes of reduced-order models that
approximately
matching the stochastic moment, are computationally tractable.