Correction to: Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes, Bernoulli 18, pp. 46-63, 2012

Robert Stelzer

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arXiv · 2411.06935

Correction to: Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes, Bernoulli 18, pp. 46-63, 2012

Robert Stelzer

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Abstract

A serious flaw in the proof of the equivalence of continuous time state space models and MCARMA processes spotted in Fasen and Schenk (2024) is corrected. We point out that likewise an issue in the proof of Theorem 3.2 in Brockwell and Schlemm (2013) can be resolved and, hence, any MCARMA process and linear state space model has both a controller and an observer canonical representation. Equivalently, the transfer function has both a left and right matrix fraction representation.

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Robert Stelzer. 2024-11-11. Correction to: Multivariate CARMA processes, continuous-time state space models and complete regularity of the innovations of the sampled processes, Bernoulli 18, pp. 46-63, 2012. https://arxiv.org/abs/2411.06935

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