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Blazar variability may be driven by stochastic processes. On the other hand,quasi-periodic oscillation (QPO) behaviors are recently reported to be detectedin $\it{Fermi}$-LAT data of blazars. However, the significances of these QPOsignals given by traditional Fourier-like methods are still questioned. Weanalyze $\gamma$-ray light curves of the QPO blazars with two Gaussian processmethods, CARMA and $\it{celerite}$, to examine the appropriateness of Gaussianprocesses for characterizing $\gamma$-ray light curves of blazars and theexistence of the reported QPOs. We collect a sample of 27 blazars with possible$\gamma$-ray periodicity and generate their $\sim11$ years $\it{Fermi}$-LATlight curves. We apply the Gaussian process models to the $\gamma$-ray lightcurves, and build their intrinsic power spectral densities (PSDs). The resultsshow that in general the $\gamma$-ray light curves can be characterized byCARMA and $\textit{celerite}$ models, indicating that $\gamma$-rayvariabilities of blazars are essentially Gaussian processes. The resulting PSDsare generally the red noise shapes with slopes between $-0.6$ and $-1.7$.Possible evidence for the $\gamma$-ray QPOs in PKS 0537$-$441 and PG 1553$+$113are found in the Gaussian process modelings.

Gaussian Process Modeling $\it{Fermi}$-LAT $\gamma$-ray Blazar Variability: A Sample of Blazars with $\gamma$-ray Quasi-periodicities