Realization Theory for Multivariate Gaussian Processes II: State Space Theory Revisited and Dynamical Representations of Finite Dimensional.

Abstract

The purpose of this paper is twofold. First, some of the results of Part I are generalized and clarified, reformulated in a mathematical framework which we now perceive as more natural and conceptually sounder, the basic concept being perpendicularly intersecting subspaces. By relating minimality of stochastic realizations to the factorization of certain Hankel operators, the connections to deterministic realization theory is further clarified. Furthermore, spectral domain criteria for minimality, observability and constructibility are presented. Secondly, stochastic differential equation representations are presented for all state spaces which are finite dimensional. The infinite dimensional case will be the topic of Part III of this sequence of papers. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1979
Accession Number
ADA078749

Entities

People

  • Anders Lindquist
  • Giorgio Picci

Organizations

  • University of Kentucky

Tags

Communities of Interest

  • Air Platforms
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Air Force
  • Algorithms
  • Data Science
  • Equations
  • Gaussian Processes
  • Information Science
  • Kentucky
  • Mathematics
  • Polynomials
  • Random Variables
  • Scientific Research
  • Sequences
  • Spectra
  • Statistical Analysis
  • Statistics
  • Stochastic Processes

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.

Technology Areas

  • Space