This paper presents a procedure for determination of dynamic properties of rolling element bearing by using the vibration signals picked up at the bearing caps. The rotor-bearing assembly is idealized as Duffing oscillator and random vibration signals modelled as exponentially correlated (Ornstein-Uhlenbeck) colored noise. Expressing the excitation as a first order filtered white noise enables the direct formulation of the 3D-Fokker Planck (FP) equation for system response through the Markov vector approach. Closed form solution of the stationary FP equation is derived. Subsequently the response statistics of experimentally obtained random vibration signal are processed through the closed form solution of the FP equation as the inverse process of parameters estimation from the measured response. Further, the dynamic behavior of rigid rotor-bearing system is investigated under combined excitation of white noise and harmonic forces arising due to rotor unbalance force. The effect of system nonlinearities, stiffness, damping and unbalanced excitation force on the dynamic response are investigated using the bifurcation plot. For assessment of structural degradation of bearings, a novel entropy based approach is developed. Experimental studies on roller bearing are carried out to demonstrate the effectiveness of the proposed approach.