  In the strong noise regime, we study the homogeneization of quantum
trajectories i.e. stochastic processes appearing in the context of quantum
measurement.
  When the generator of the average semi-group can be separated into three
distinct time scales, we start by describing a homogenized limiting semi-group.
This result is of independent interest and is formulated outside of the scope
of quantum trajectories.
  Going back to the quantum context, we show that, in the Meyer-Zheng topology,
the time-continuous quantum trajectories converge weakly to the discontinuous
trajectories of a pure jump Markov process. Notably, this convergence cannot
hold in the usual Skorokhod topology.
