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The noise-free CMOS inverter is described by a first- order non-linear differential equation that can be regarded as a standard case in electronic circuits from the system-theoretic viewpoint. In lieu of the noise-free CMOS inverter, this paper explains the stochastic CMOS inverter at the low power supply voltage. The method of this paper utilizes the Kolmogorov-Fokker-Planck equation for the noise analysis of the CMOS inverter. In this paper, first we develop the CMOS inverter Itô Stochastic Differential Equation (SDE). Secondly, a system of two-coupled state estimation equations is derived. The numerical experimentations are demonstrated for the noise analysis of the CMOS inverter circuits as well.