On Minimal Splitting Subspaces and Markovian Representations.

Abstract

Given a Hilbert space H, let H sub 1 and H sub 2 be two arbitrary subspaces. The problem of finding all minimal splitting subspaces with respect to H sub 1 and H sub 2 is solved. The result is applied to the stochastic realization problem. Each minimal stochastic realization of a given vector process y defines a family of state spaces. It is shown that these families are precisely those families of minimal splitting subspaces (with respect to the past and the future of y) which satisfy a certain growing condition.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1978
Accession Number
ADA072624

Entities

People

  • Anders Lindquist
  • Giorgio Picci
  • Guy Ruckebusch

Organizations

  • University of Kentucky

Tags

DTIC Thesaurus Topics

  • Air Force
  • Applied Mathematics
  • Data Science
  • Gaussian Processes
  • Hilbert Space
  • Information Science
  • Inverse Problems
  • Kentucky
  • Markov Processes
  • Mathematics
  • Probability
  • Random Variables
  • Stationary Processes
  • Stochastic Processes
  • United States
  • United States Government
  • White Noise

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space