EQUIVALENCE PROBLEMS FOR GAUSSIAN MULTIPLE MARKOV-PROCESSES AND THEIR CANONICAL REPRESENTATIONS

We obtain a necessary and sufficient condition for two given Gaussian multiple Markov processes to be equivalent. In case they are equivalent, the Radon-Nikodym density can be expressed in terms of the kernels of their canonical representations. As a development, equivalence of two random fields is discussed assuming that they are in a certain class of isotropic Gaussian fields. It is further shown that such an approach is successful for N-ple Markov Gaussian processes with multiplicity N (N greater-than-or-equal-to 1) within our framework.