  In this paper we investigate some general aspects of fluctuation and
dissipation in the holographic scenario at zero and finite density. We model
this situation with a probe string in a diagonal metric representing a black
brane. The string stretches from the black brane to a probe brane thus
simulating a stochastic driven particle. In this scenario, we compute the
admittance, the diffusion coefficient, the correlation functions and the
regularized mean square displacement, for bosons and fermions, all from the
metric components. We check these calculations with the fluctuation-dissipation
theorem. Further, we show that at finite temperature and density, the mean
square displacement in the limit of short times reproduces the usual quadratic
(ballistic) behavior, for bosons and fermions. For large times, we find
ultraslow diffusive processes in various cases, except for bosons at zero
chemical potential. We apply this general analysis in two different models:
hyperscaling violation at finite temperature and a charged dilatonic AdS black
hole, both for bosons and fermions. This is important because we found the
fermionic diffusion in systems which allow the appearance of Fermi surfaces and
Fermi liquids.
