| Summary: | We consider a jump Markov process X=(Xt)t≥0X={\left({X}_{t})}_{t\ge 0}, with values in a state space (E,ℰ)\left(E,{\mathcal{ {\mathcal E} }}). We suppose that the corresponding infinitesimal generator πθ(x,dy),x∈E{\pi }_{\theta }\left(x,{\rm{d}}y),x\in E, hence the law Px,θ{{\mathbb{P}}}_{x,\theta } of XX, depends on a parameter θ∈Θ\theta \in \Theta . We prove that several models (filtered or not) associated with XX are linked, by their regularity according to a certain scheme. In particular, we show that the regularity of the model (πθ(x,dy))θ∈Θ{\left({\pi }_{\theta }\left(x,{\rm{d}}y))}_{\theta \in \Theta } is equivalent to the local regularity of (Px,θ)θ∈Θ{\left({{\mathbb{P}}}_{x,\theta })}_{\theta \in \Theta }.
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