Before revision:  In the first case, the noise is multiplicative and symmetric, and we conclude that the fluctuations of the degradation reaction rate induce different switching processes for different noise param- eters.For the second case, the noise is additive and asymmetric, and we find that the fluctuations of the synthesis reaction rate lead to interesting transitions. The mean first exit time can be shortened and first escape probability can be increased by adjusting the noise parameters.
After revision:  In the first case, the noise is multiplicative and symmetric, and we conclude that the fluctuations of the synthesis reaction rate lead to peculiar transitions to higher concentrations (i.e., higher likelihood for transcriptions), such as higher likelihood of transcription for larger positive skewness parameter (asymmetry index) \beta, achieving the minimum likelihood of transcription by tuning skewness parameter \beta, achieving the higher likelihood of transcription by tuning non-Gaussianity index \alpha, and a bifurcation for transcription at the critical value \alpha=1. We conduct a series of numerical experiments about `regulating' the likelihood of gene transcription by tuning asymmetric stable L\'evy noise parameters.