Non-equilibrium plasma has garnered significant attention due to its involvement in short-term phenomena. One example is plasma fluctuation, encompassing variations in electron temperature or density. This phenomenon is explored not only in nuclear fusion but also in semiconductor etching and thin film deposition. This study introduces an evaluation method employing Malliavin derivatives to predict plasma fluctuations based on a collisional-radiative model. This model delineates the chemical kinetics of excited states within the plasma. Given that electron impact excitation and atomic collisional processes are stochastic, they exhibit characteristics similar to a Wiener process. Furthermore, the properties of fractional Brownian motion are applied to the Malliavin derivative. The revised Wiener process is utilized to analyze the changes in excited-level populations within short durations. This approach assesses electron or atomic density fluctuations by considering the contributions of electron collisions and those of ground-state atoms.
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