Continuous parameter circuit processes with finite state space

Given a finite set S, a class of overlapping directed circuits in S and a collection of weight functions wc:[0,+[infinity])-->[0,+[infinity]), c[epsilon], that verify certain topological and algebraic relations, we uniquely define a continuous parameter Markov process ([xi]t)t[greater-or-equal, slanted]0 called a circuit process. The constructive solution to a correspondence ([xi]t)t[greater-or-equal, slanted]0-->{, wc}, which becomes one-to-one when {, wc} can be given a probabilistic interpretation, is described. In particular we show that the Lévy-Austin-Ornstein theorem concerning the positiveness of the transition probabilities pij(·) is a qualitative property. Also it is proved that the intensities qij have a probabilistic interpretation in terms of the sample paths of the discrete skeletons. Finally, analytical properties of the weight functions are studied.