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.
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References
P.J. Brockwell, R.A. Davis, Time Series: Theory and Methods (Springer, New York, 1987)
P.E. Caines, Linear Stochastic Systems (Wiley, New York, 1988)
I. Gohberg, P. Lancaster, L. Rodman, Matrix Polynomials (Academic Press, New York, 1982)
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Heij, C., C.M. Ran, A., van Schagen, F. (2021). Stochastic Systems. In: Introduction to Mathematical Systems Theory. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-59654-5_6
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DOI: https://doi.org/10.1007/978-3-030-59654-5_6
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Publisher Name: Birkhäuser, Cham
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