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.

翻译：本文修正了在Fasen和Schenk（2024）中指出的关于连续时间状态空间模型与MCARMA过程等价性证明中的一个严重缺陷。我们指出，Brockwell和Schlemm（2013）中定理3.2证明中的一个问题同样可以得到解决，因此，任何MCARMA过程和线性状态空间模型均同时具有控制器规范型和观测器规范型。等价地，其传递函数同时具有左矩阵分式表示和右矩阵分式表示。