On the Stochastic Realization Problem. Revision.
Abstract
Given a mean-square continuous stochastic vector process y with stationary increments and a rational spectral density Phi such that Phi(infinity) is finite an nonsingular, consider the problem of finding all minimal Gauss-Markov representations (stochastic realizations) of y. All such realizations are characterized and classified with respect to deterministic as well as probabilistic properties. It is shown that only certain realizations (internal Stochastic realizations) can be determined from the given output process y. All others (external stochastic realizations) require that the probability space be extended with an exogeneous random component. A complete characterization of the sets of internal and external stochastic realizations is provided. It is shown that the state process of any internal stochastic realization can be expressed in terms of two steady-state Kalman-Bucy filters, one evolving forward in time over the infinite past and one backward over the infinite future. An algorithm is presented which generates families of external realizations defined on the same probability space and totally ordered with respect to state covariances. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1978
- Accession Number
- ADA060418
Entities
People
- Anders Lindquist
- Giorgio Picci
Organizations
- University of Kentucky