Accession Number:

ADA073230

Title:

A State-Space Theory for Stationary Stochastic Processes,

Descriptive Note:

Corporate Author:

KENTUCKY UNIV LEXINGTON DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1978-01-01

Pagination or Media Count:

8.0

Abstract:

Consider a stationary Gaussian stochastic process ytt an element of R with a rational spectral density, and let Hy be the Hilbert space spanned by it. The problem of determining all stationary and purely nondeterministic families of minimal splitting subspaces of Hy is considered the splitting subspaces constitute state-spaces for the process y. It is shown that some of these families are Markovian, and they lead to internal stochastic realizations. A complete characterization of all Markovian and non-Markovian families of minimal splitting subspaces is provided. Many of the basic results hold without the assumption of rational spectral density. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE