  High-resolution radio observations of nearby active galactic nuclei have
revealed extended, limb-brightened structures in their inner jets. This ties in
with other multi-wavelength observations from radio to X-ray and gamma-ray,
indicating that a structured jet model is required. While electrons need to be
kept energized to account for the observed features, the underlying particle
acceleration mechanism is still unclear. We explore the role of stochastic
Fermi-type particle acceleration, i.e., classical second-order Fermi and shear
acceleration, for understanding the multi-wavelength observations of the inner
jets of M87. An analytical Fokker-Planck description is adopted to infer
characteristic spectral indices and cutoff energies for these two mechanisms.
We focus on electron synchrotron radiation as the dominant emission process. We
find that the multi-wavelength observations of M87 can be satisfactorily
accounted for in a framework, where the X-rays are produced at a larger
distance from the core than the radio emission region. This provides further
support to multi-zone, broadband emission modelling. We use our findings to
also comment on the acceleration of cosmic rays entrained in the sheath.
