Evaluating the influence of noise on the spectrum of an oscillator

Phase models are practical tools to investigate the phase noise in stochastic oscillators. Traditional phase models describe the phase noise problem as a diffusion process, but experiments and simple solvable models reveal that white noise can also induce a frequency shift in the spectra of oscillators. In this paper we explain why traditional phase models fail to capture noise induced frequency shift and we present an improved phase model that explains this phenomenon. We develop a method for the direct calculation of the mean oscillation frequency and the power spectral density of stochastic oscillators. Our method can be applied to a wide class of stochastic oscillators.