Abstract
We consider a jump Markov process X = (X-t)(t >= 0), with values in a state space (E, epsilon). We suppose that the corresponding infinitesimal generator pi(theta)(x, dy), x is an element of E, hence the law P-x,P-theta of X, depends on a parameter theta E Theta. We prove that several models (filtered or not) associated with X are linked, by their regularity according to a certain scheme. In particular, we show that the regularity of the model (pi(theta)(x, dy))(theta is an element of Theta) is equivalent to the local regularity of (P-x,P-theta)(theta is an element of Theta).