Phase noise in oscillators according to the ISF theory is cyclostationary. According to this theory, noise impulse at any point of time will be integrated weighted by the impulse sensitivity function, which is usually highest during the zero crossings of the oscillator output. Clearly, phase noise is a continuous time phenomenon.
But when we model phase noise we treat it as a integrated timing errors only at the zero crossing of the oscillators and treat it as a discrete process (Ref: Simulation and Modeling of Phase Noise in Open-Loop Oscillators, Alper Demir). Not only this, the oscillator is now treated just as an integrator which is an LTI system.
Could someone please explain why treating the oscillator as LTI system is justified and why considering just the timing errors at the zero crossings is sufficient to calculate phase noise?