The standard continuous time state space model with stochastic
disturbances contains
the mathematical abstraction of continuous time white noise. To
work with well defined,
discrete time observations, it is necessary to sample the model with
care. The basic
issues are well known, and have been discussed in the literature.
However, the
consequences have not quite penetrated the practise of estimation
and identification.
One example is that the standard model of an observation being a
snapshot of the
current state plus noise independent of the state cannot be
reconciled with this picture.
Another is that estimation and identification of time continuous
models require a more
careful treatment of the sampling formulas. We discuss and illustrate
these issues in the
current contribution. An application of particular practical
importance is the estimation
of models based on irregularly sampled observations.