A State-Space Theory for Stationary Stochastic Processes,

Abstract

Consider a stationary Gaussian stochastic process (y(t);t an element of R) with a rational spectral density, and let H(y) be the Hilbert space spanned by it. The problem of determining all stationary and purely nondeterministic families of minimal splitting subspaces of H(y) 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)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1978
Accession Number
ADA073230

Entities

People

  • Anders Lindquist
  • Giorgio Picci

Organizations

  • University of Kentucky

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Hilbert Space
  • Inverse Problems
  • Kentucky
  • Mathematics
  • New York
  • Polynomials
  • Probability
  • Scientific Research
  • Security
  • Splitting
  • Stationary
  • Stationary Processes
  • Steady State
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space
  • Space - Hall-Effect Thruster