Before revision:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP),  to examine the transition events from low to high concentration state under the influence of L\'evy noise.We find that the fluctuations of the synthesis reaction rate lead to peculiar transitions to higher concentrations (i.e., higher likelihood for transcriptions)
After revision:  We compute two deterministic quantities, the mean first exit time (MFET) and the first escape probability (FEP), to examine the transition events from low to high concentration states (corresponding to likelihood for transcription). By focusing on the impact of skewness (i.e., non-symmetry) in the probability distributions of noise, we find that the fluctuations of the synthesis reaction rate lead to peculiar transitions to higher concentrations (i.e., higher likelihood for transcriptions)