Stochastic Linear Models. (Modeles Stochastiques Lineaires),

Abstract

External (i.e. via covariances) and internal (i.e. via a Markov porcess) descriptions of gaussian stochastic processes are explained. The canonical decomposition of stationary Markov processes in purely nondeterministic and purely deterministic parts is given and is shown to be closely related to the decomposition of a linear system in controllable and noncontrollable parts. Then an algorithm solving the positive real lemma giving a Markovian representation of a stochastic process is given. This algorithm is essentially a Riccati-type equation and is superior to classical factorization methods in the multi-dimensional case. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1970
Accession Number
AD0722468

Entities

People

  • P. Faurre

Organizations

  • Mines ParisTech

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Covariance
  • Decomposition
  • Equations
  • Linear Systems
  • Markov Processes
  • Mathematics
  • Stationary
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Linear Algebra
  • Mathematical Modeling and Probability Theory.