  We point to the connection between a recently introduced class of
non-Markovian master equations and the general structure of quantum collisional
models. The basic construction relies on three basic ingredients: a collection
of time dependent completely positive maps, a completely positive trace
preserving transformation and a waiting time distribution characterizing a
renewal process. The relationship between this construction and a Lindblad
dynamics is clarified by expressing the solution of a Lindblad master equation
in terms of demixtures over different stochastic trajectories for the
statistical operator weighted by suitable probabilities on the trajectory
space.
