Moment-Linear Stochastic Systems

We introduce a class of quasi-linear models for stochastic dynamics, called moment-linear stochastic systems (MLSS). We formulate MLSS and analyze their dynamics, as well as discussing common stochastic models that can be represented as MLSS. Further studies, including development of optimal estimators and controllers, are summarized. We discuss the reformulation of a common stochastic hybrid system—the Markovian jumplinear system (MJLS)—as an MLSS, and show that the MLSS formulation can be used to develop some new analyses for MJLS. Finally, we briefly discuss the use of MLSS in modeling certain stochastic network dynamics. Our studies suggest that MLSS hold promise in providing a framework for modeling interesting stochastic dynamics in a tractable manner.