Continuous measurement models are conveniently based on master equatio
ns specified by the respective Hamiltonian and appropriate environment
operators. As demonstrated by stochastic unraveling, the latter speci
fy the dynamical process rather than static detection modes. We show t
hat certain environment operators acting on a simple system may, in fa
ct, require extended networks for implementation: Their Hamilton param
eters re-appear in the effective environment operators of the reduced
model. The resulting quantum trajectories typically involve competing
paths, which may give rise to different fluctuation and noise properti
es even when the corresponding ensemble behavior is practically the sa
me.