  We study the stochastic motion of a relativistic trailing string in black
hole AdS_5. The classical string solution develops a world-sheet horizon and we
determine the associated Hawking radiation spectrum. The emitted radiation
causes fluctuations on the string both above and below the world-sheet horizon.
In contrast to standard black hole physics, the fluctuations below the horizon
are causally connected with the boundary of AdS. We derive a bulk stochastic
equation of motion for the dual string and use the AdS/CFT correspondence to
determine the evolution a fast heavy quark in the strongly coupled $\N=4$
plasma. We find that the kinetic mass of the quark decreases by $\Delta
M=-\sqrt{\gamma \lambda}T/2$ while the correlation time of world sheet
fluctuations increases by $\sqrt{\gamma}$.
