  We review equilibrium properties for the dynamics of a single particle
evolving in a visco--elastic medium under the effect of hydrodynamic backflow
which includes added mass and Basset force. Arbitrary equilibrium forces acting
upon the particle are also included. We discuss the derivation of the explicit
expression for the thermal noise correlation function that is consistent with
the fluctuation-dissipation theorem. We rely on general time-reversal arguments
that apply irrespective of the external potential acting on the particle, but
also allow one to retrieve existing results derived for free particles and
particles in a harmonic trap. Some consequences for the analysis and
interpretation of single-particle tracking experiments are briefly discussed.
