Moment Lyapunov Exponent and Stability Index for Linear Conservative System with Small Random Perturbation

Asymptotic expansion series for the moment Lyapunov exponent and stability index are constructed and justified for the two-dimensional linear stochastic system close to a harmonic oscillator. As an example, a one-degree-of-freedom mechanical system parametrically excited in stiffness and damping is considered and several terms of the expansion are obtained.