  We use an effective Markovian description to study the long-time behaviour of
a nonlinear second order Langevin equation with Gaussian noise. When
dissipation is neglected, the energy of the system grows as with time a
power-law with an anomalous scaling exponent that depends both on the confining
potential and on the high frequency distribution of the noise. The asymptotic
expression of the Probability Distribution Function in phase space is
calculated analytically. The results are extended to the case where small
dissipative effects are taken into account.
