  Stochastic acceleration of cosmic rays in second order Fermi processes is
usually considered too slow to reach ultra-high energies, except in specific
cases. In this paper we present the energy spectrum obtained from second order
Fermi acceleration in highly turbulent magnetic fields as e.g.\ found in the
outskirts of AGN jets in situations where it can be sufficiently fast to
accelerate particles to the highest observed energies. We parametrize the
resulting non-power-law spectra and show that these can describe the cosmic ray
energy spectrum and mass-composition data at the highest energies if
propagation effects are taken into account.
