Oscillator Noise: A Nonlinear Perturbative Theory Including Orbital Fluctuations and Phase-Orbital Correlation

We derive a full statistical characterization of the noise spectrum of a free running oscillator perturbed by white Gaussian noise sources, including the effect of orbital fluctuations and of their correlation with phase noise, thus extending the previous theory based on the Floquet decomposition of the linearized oscillator equations . This allows to derive explicit relationships for the relevant phase, amplitude and correlation spectra. The examples provide a validation of the theoretical results, and allow to assess the importance of the Floquet exponents and eigenvectors on the magnitude of the orbital noise contribution.