Perturbation of system dynamics and the covariance completion problem

We consider the problem of completing partially known sample statistics in a way that is consistent with underlying stochastically driven linear dynamics. Neither the statistics nor the dynamics are precisely known. Thus, our objective is to reconcile the two in a parsimonious manner. To this end, we formulate a convex optimization problem to match available covariance data while minimizing the energy required to adjust the dynamics by a suitable low-rank perturbation. The solution to the optimization problem provides information about critical directions that have maximal effect in bringing model and statistics in agreement.