State Space Models for Gaussian Stochastic Processes.

Abstract

A comprehensive theory of stochastic realization for multivariate stationary Gaussian processes is presented. It is coordinate-free in nature, starting out with an abstract state space theory in Hilbert space, based on the concept of splitting subspace. These results are then carried over to the spectral domain and described in terms of Hardy functons. Each state space is uniquely characterized by its structural function, an inner function which contains all the systems theoretical characteristics of the corresponding realizations. Finally coordinates are introduced and concrete differential-equation-type representations are obtained. This paper is an abridged version of a forthcoming paper, which in turn summarizes and considerably extends results which have previously been presented in a series of preliminary conference papers. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 05, 1980
Accession Number
ADA092388

Entities

People

  • Anders Lindquist
  • Giorgio Picci

Organizations

  • University of Kentucky

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Applied Mathematics
  • Concrete
  • Construction
  • Data Science
  • Differential Equations
  • Equations
  • Fokker Planck Equations
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • Markov Processes
  • Mathematics
  • Random Variables
  • Stationary Processes
  • Stochastic Processes

Readers

  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.

Technology Areas

  • Space