  We study a stochastic Schroedinger equation that generates a family of
Gaussian dynamical maps in one dimension permitting a detailed exam of two
different definitions of non-Markovianity: one related to the explicit
dependence of the generator on the starting time, the other to the
non-divisibility of the time-evolution maps. The model shows instances where
one has non-Markovianity in both senses and cases when one has Markovianity in
the second sense but not in the first one.
