  We study the generalization of the QMUPL model which accounts both for memory
and dissipative effects. This is the first model where both features are
combined. After having derived the non-local Action describing the system, we
solve the equation for a quantum harmonic oscillator via the path integral
formalism. We give the explicit expression for the Green's function of the
process. We focus on the case of an exponential correlation function and we
analyze in detail the behavior Gaussian wave functions. We eventually study the
collapse process, comparing the results with those of previous models.
