Emergence of Jumps in Quantum Trajectories via Homogenization

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