Based on a generalized Langevin equation, we consider a full general relativistic model to describe the vertical oscillations of particles in accretion disks around compact astrophysical objects, and calculate oscillating luminosity and power spectral density (PSD) of an accretion disk. The influences of the friction parameter 𝜁, spin parameter 𝑎* and mass 𝑀 of the center compact object on the stochastic resonance (SR) in PSD curves are discussed. The results show that a large spin parameter 𝑎* can enhance the SR phenomenon, but the larger the 𝜁 or 𝑀 is, the weaker the SR phenomenon becomes. In addition, our simulated PSD curves of the output luminosity of stochastically oscillating disk have the same profile as the observed PSD of x-ray binaries, and the resonance peak in the PSD curve can interpret the quasi-periodic oscillations at the same time.

By using a generalized Langevin equation to describe the vertical oscillations of a general relativistic disk subjected to a memory-damped friction and a stochastic force, we derive the power spectrum density (PSD) of accretion disk oscillating luminosity by the method of Laplace transform, and discuss the influence of the system parameters on the resonant behavior in PSD curves. The results show that as the damping strength α and memory time τ of the friction increase, the variation of PSD with spectrum frequency f from monotonous decreasing to occurring maximums, and the phenomenon of a general stochastic resonance (SR) with a single peak and multi-peaks can be found in PSD curves. The radial distance parameter n, the mass M, and spin parameter a * of the black hole determine the inherent frequency of vertical oscillations in the disk, and they have significant influences on the SR phenomena in a system of black hole binaries.

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