Stochastic Systems

Christiaan Heij (), André C.M. Ran () and Frederik van Schagen ()
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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

Chapter 6 in Introduction to Mathematical Systems Theory, 2021, pp 81-99 from Springer

Abstract: 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.

Date: 2021
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DOI: 10.1007/978-3-030-59654-5_6

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