The Covariance Extension Equation Revisited

The Covariance Extension Equation Revisited

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by Christopher I. Byrnes , Giovanna Fanizza , Anders Lindquist

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@MISC{Byrnes_thecovariance,
    author = {Christopher I. Byrnes and Giovanna Fanizza and Anders Lindquist},
    title = {The Covariance Extension Equation Revisited},
    year = {}
}

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Abstract

Abstract — In this paper we study the steady state form of a discrete-time matrix Riccati-type equation, connected to the rational covariance extension problem and to the partial stochastic realization problem. This equation, however, is nonstandard in that it lacks the usual kind of definiteness properties which underlie the solvability of the standard Riccati equation. Nonetheless, we prove the existence and uniqueness of a positive semidefinite solution. We also show that this equation has the proper geometric attributes to be solvable by homotopy continuation methods, which we illustrate in several examples. Let I.

Citations

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