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In the strong noise regime, we study the homogeneization of quantumtrajectories i.e. stochastic processes appearing in the context of quantummeasurement.  When the generator of the average semi-group can be separated into threedistinct time scales, we start by describing a homogenized limiting semi-group.This result is of independent interest and is formulated outside of the scopeof 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 discontinuoustrajectories of a pure jump Markov process. Notably, this convergence cannothold in the usual Skorokhod topology.

Emergence of jumps in quantum trajectories via homogeneization