ON SAMPLING OF CONTINUOUS-TIME STOCHASTIC-PROCESSES

Techniques for sampling of continuous time stochastic processes are presented. To obtain flexible models and well-posed filtering problems, we assume an underlying continuous time innovations model. To sample such a model ''averaged sampling'' is applied. It is shown that this technique is equivalent to the following two step procedure: Determine by instantaneous (direct) sampling a discrete model for the continuous time process obtained by integrating the original innovations model. Then differentiate the sampled process to remove the discrete pole at z = 1 introduced by the integration. An advantage with this procedure is that one obtains ARMA(n, n) models, while instantaneous sampling only gives ARMA(n, n - 1) models. Furthermore, the problem of updating discrete time models, without using a continuous time model, in case of a change of sampling rate-decimation/interpolation-is addressed.