  A stochastic model is proposed for the acceleration of non-relativistic
particles yielding to energy spectra with a shape of a Weibull\textquoteright s
function. Such particle distribution is found as the stationary solution of a
diffusion-loss equation in the framework of a second order Fermi\textquoteright
s mechanism producing anomalous diffusion for particle velocity. The present
model is supported by in situ observations of energetic particle enhancements
at interplanetary shocks, as here illustrated by means of an event seen by
STEREO B instruments in the heliosphere. Results indicate that the second order
Fermi\textquoteright s mechanism provides a viable explanation for the
acceleration of energetic particles at collisioness shock waves.
