  We analyze the general relativistic oscillations of thin accretion disks
around compact astrophysical objects interacting with the surrounding medium
through non-gravitational forces. The interaction with the external medium (a
thermal bath) is modeled via a friction force, and a random force,
respectively. The general equations describing the stochastically perturbed
disks are derived by considering the perturbations of trajectories of the test
particles in equatorial orbits, assumed to move along the geodesic lines. By
taking into account the presence of a viscous dissipation and of a stochastic
force we show that the dynamics of the stochastically perturbed disks can be
formulated in terms of a general relativistic Langevin equation. The stochastic
energy transport equation is also obtained. The vertical oscillations of the
disks in the Schwarzschild and Kerr geometries are considered in detail, and
they are analyzed by numerically integrating the corresponding Langevin
equations. The vertical displacements, velocities and luminosities of the
stochastically perturbed disks are explicitly obtained for both the
Schwarzschild and the Kerr cases.
