Stochastic Realization

Jan H. van Schuppen*

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedings/Edited volumeChapterScientific


Stochastic realization problems are presented for a tuple of Gaussian random variables, for a tuple of σ -algebras, for a σ -algebra family, and for a finite stochastic system. The solution of the weak and of the strong stochastic realization of a tuple of Gaussian random variables is provided. The main theoretical contribution is the description of the strong stochastic realization of a tuple of σ -algebras. This is followed by stochastic realization of a family of σ -algebras. Finally the stochastic realization problem for finite-valued output processes is discussed.

Original languageEnglish
Title of host publicationControl and System Theory of Discrete-Time Stochastic Systems
Number of pages62
ISBN (Electronic)978-3-030-66952-2
Publication statusPublished - 2021

Publication series

NameCommunications and Control Engineering
ISSN (Print)0178-5354
ISSN (Electronic)2197-7119


  • Stochastic realization
  • σ -algebraic system


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