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We introduce a simple stochastic system able to generate anomalous diffusionboth for position and velocity. The model represents a viable description ofthe Fermi's acceleration mechanism and it is amenable to analytical treatmentthrough a linear Boltzmann equation. The asymptotic probability distributionfunctions (PDF) for velocity and position are explicitly derived. The diffusionprocess is highly non-Gaussian and the time growth of moments is characterizedby only two exponents $\nu_x$ and $\nu_v$. The diffusion process is anomalous(non Gaussian) but with a defined scaling properties i.e. $P(|{\bf x}|,t) =1/t^{\nu_x}F_x(|{\bf x}|/t^{\nu_x})$ and similarly for velocity.Comment: RevTeX4, 4 pages, 2 eps-figures (minor revision

Minimal Stochastic Model for Fermi’s Acceleration