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It is a well-known, yet poorly understood fact that, contrary to the continuous-time case, the same discrete-time process y can be represented by minimal linear models (see (1.1a), (1.1b) below) which may either have a non-singular or a singular D matrix. In fact, models with D=0 have been commonly used in the statistical literature. On the other hand, for models with a singular D matrix the Riccati...
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