A stochastic model is proposed for the acceleration of non-relativistic particles yielding to energy spectra with a shape of a Weibulltextquoteright s function. Such particle distribution is found as the stationary solution of a diffusion-loss equation in the framework of a second order Fermitextquoteright 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 Fermitextquoteright s mechanism provides a viable explanation for the acceleration of energetic particles at collisioness shock waves.
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