  We analyze in details how the anomalous drift and diffusion properties of a
particle evolving in an aging medium can be interpreted in terms of an
effective temperature of the medium. From an experimental point of view,
independent measurements of the mean-square displacement and of the mobility of
a particle immersed in an aging medium such as a colloidal glass give access to
an out of equilibrium generalized Stokes-Einstein relation, from which the
effective temperature of the medium can eventually be deduced. We illustrate
the procedure on a simple model with power-law behaviours.
