On the Markov property for certain Gaussian random fields
It is well known that the so-called Markov property for random fields is an important ingredient in quantum field theory. Gaussian random fields associated with symmetric Markov processes were studied by E. B. Dynkin, who proved that the Markov property is at hand for the random field iff the Markov process has continuous paths. Later, \textit{M. Röckner} [see Math. Ann. 264, 153-177 (1983; Zbl 0519.60047)] gave an analytic proof of the same result in a slightly different formulation using the framework of Dirichlet spaces. In our article, a very simple proof of this result is presented. The main point is to use the ''fine topology'', and this is based on earlier results of the author. We also treat the connection between these random fields and certain infinite dimensional Ornstein- Uhlenbeck processes.
infinite dimensional Ornstein-Uhlenbeck processes
scientific article; zbMATH DE number 3951705
scientific article