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Stochastic Systems

In: Introduction to Mathematical Systems Theory

Author

Listed:
  • Christiaan Heij

    (Erasmus University Rotterdam, Department of Econometrics)

  • André C.M. Ran

    (Vrije Universiteit, Department of Mathematics)

  • Frederik van Schagen

    (Vrije Universiteit, Department of Mathematics)

Abstract

In stochastic systems, the outputs are (partly) driven by unobserved random inputs. This chapter is concerned with stationary processes and their approximation with finite dimensional linear stochastic systems. Similar to the results for deterministic input-output systems there is an equivalence between finite dimensional stochastic state space models, polynomial (ARMA) representations, and rational spectra (in the frequency domain), which are the analogue of the transfer function.

Suggested Citation

  • Christiaan Heij & André C.M. Ran & Frederik van Schagen, 2021. "Stochastic Systems," Springer Books, in: Introduction to Mathematical Systems Theory, edition 2, chapter 6, pages 81-99, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-59654-5_6
    DOI: 10.1007/978-3-030-59654-5_6
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