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Random walk noise is an important component in the output phase noise of a voltage-controlled oscillator (VCO). The relation between this non-stationary noise component and the induced timing jitter is critical for VCO performance characterization. Rigorous derivation of the relation is provided in this paper, which corrects the error in the relation obtained under wide-sense stationary assumption. Besides, the correct expression of power spectral density of the output phase noise is obtained. Additionally, discussion is provided in this paper on the measurement principle to obtain power spectral density of non-stationary phase noise.