Partial stochastic realization in finite dimensional spaces

Abstract

In this paper, we develop a new framework for partial stochastic realization in a finite dimensional space where geometric operations are performed so that the positive realness of covariance functions in a finite interval is guaranteed. To this end, we present a deterministic interpretation on the partial stochastic realization. We give necessary and sufficient conditions for positive realness based on Riccati equations, and derive a solution of the partial stochastic realization problem.