Convergence of filtered statistical models and Hellinger processes

In Jacod (1989) we have introduced the family of Hellinger processes associated with a filtered statistical experiment. Here we are concerned with the (weak) convergence of such experiments, expressed in terms of their Hellinger processes, in the case where the limiting experiment has deterministic Hellinger processes: this apparently very restrictive hypothesis covers in fact most applications, such as Gaussian shift experiments, and Poisson experiments.