Phase noise derivation in Book “High-Purity Oscillators” (A.A.)

In the book, chapter three, almost all phase noise results like equation (49) (page 57) contains 1/(Δω)2 term. This term, in Abidi’s book, is obtained from multiplying noise current and lossy tank impedance. The latter item contains 1/(Δω)2 term.

However, in some other papers, it is stated that 1/(Δω)2 term comes from integration over time operation. Since a oscillator is a system with memory, any perturbation could either be rejected as AM noise or get memorized as PM noise. Thus, any noise source would get a noise power transfer function as 1/s2. When show up in the phase noise results, it will have a term as 1/(Δω)2.

Why Abidi’s derivation does not assume this integration property, and get the same form of results?

Thanks,
Neo