A natural definition of the Markov property for multi-parameter random processes (random fields) is the following. Let {Xt, tEIR N} be a multiparameter process. For any set D in N. N, let a D denote the a-field generated by {Xt, tED}. The field {Xt, tEN. u} is said to be Markov (or Markov of degree 1 [6], or sharp Markov) if, for any bounded open set D with smooth boundary, oD and ape are condi...
