  The description of Fermi acceleration developing in the phase-randomized
simplified Fermi-Ulam model (SFUM) can be achieved in terms of a random walk
taking place in momentum space. Within this framework the evolution of the
probability density function of particle velocities is determined by the
Fokker-Planck equation (FPE). However, the standard treatment in the literature
leads to a result, which even though is in agreement with the numerical
results, it is inconsistent with the transport coefficients used for the
construction of the FPE. In this work we present a consistent scheme for the
description of Fermi acceleration, resolving this contradiction.
