  This paper is devoted to generalize some previous results presented in Gaioli
et al., Int. J. Theor. Phys. 36, 2167 (1997). We evaluate the autocorrelation
function of the stochastic acceleration and study the asymptotic evolution of
the mean occupation number of a harmonic oscillator playing the role of a
Brownian particle. We also analyze some deviations from the Bose population at
low temperatures and compare it with the deviations from the exponential decay
law of an unstable quantum system.
