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We consider a description of the stochastic oscillations of the generalrelativistic accretion disks around compact astrophysical objects interactingwith their external medium based on a generalized Langevin equation withcolored noise, which accounts for the general memory and retarded effects ofthe frictional force, and on the fluctuation-dissipation theorem. The presenceof the memory effects influences the response of the disk to external randominteractions, and modifies the dynamical behavior of the disk, as well as theenergy dissipation processes. The generalized Langevin equation of the motionof the disk in the vertical direction is studied numerically, and the verticaldisplacements, velocities and luminosities of the stochastically perturbeddisks are explicitly obtained for both the Schwarzschild and the Kerr cases.The Power Spectral Distribution (PSD) of the disk luminosity is also obtained.As a possible astrophysical application of the formalism we investigate thepossibility that the Intra Day Variability (IDV) of the Active Galactic Nuclei(AGN) may be due to the stochastic disk instabilities. The perturbations due tocolored/nontrivially correlated noise induce a complicated disk dynamics, whichcould explain some astrophysical observational features related to diskvariability.

Generalized Langevin equation with colored noise description of the stochastic oscillations of accretion disks