Hokkaido University Preprint Series in Mathematics
We discuss Gaussian generalized random fields indexed by smooth sections of vector bundles with respect to Markov properties. We propose a new set-up which is suitable for the present question and within which new phenomena are detected naturally. In particular, we give a counterexample to the belief that locality in the RKHS implies germ Markov property. We also prove the close connection between Markov property and cokernels of local operators.