TY - CHAP
T1 - Stochastic Realization
AU - van Schuppen, Jan H.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
KW - Stochastic realization
KW - σ -algebraic system
UR - http://www.scopus.com/inward/record.url?scp=85112492070&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-66952-2_7
DO - 10.1007/978-3-030-66952-2_7
M3 - Chapter
AN - SCOPUS:85112492070
T3 - Communications and Control Engineering
SP - 231
EP - 292
BT - Control and System Theory of Discrete-Time Stochastic Systems
PB - Springer
ER -