  We analyze the non-Markovian stochastic Schroedinger equation describing a
particle subject to spontaneous collapses in space (in the language of collapse
models), or subject to a continuous measurement of its position (in the
language of continuous quantum measurement). For the first time, we give the
explicit general solution for the free particle case (H = p^2/2m), and discuss
the main properties. We analyze the case of an exponential correlation function
for the noise, giving a quantitative description of the dynamics and of its
dependence on the correlation time.
