Stochastic Realization

Book chapter (2021)

Authors

J.H. van Schuppen Mathematical Physics - EEMCS
Research Group
Mathematical Physics (EEMCS) (TU Delft)
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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

Abstract

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.