Higher-order statistics of a bistable system driven by dichotomous colored noise.

Exact expressions for first- and higher-order residence time statistics, count statistics, and spectral properties of a bistable system driven by dichotomous colored noise are put forward and discussed. The employed method is based on a discrete kinetic scheme and is valid for a wide range of parameter values of the colored noise. This permits a detailed analysis of the effects of noise correlations for arbitrary correlation times. It is found that at a characteristic correlation time of the dichotomous noise, the residence time sequence becomes Poissonian; in particular, all correlations between residence times disappear. We also find that correlations become strongest for a finite strength of the driving force. The analytical results can also be used to infer the underlying driving parameters in the case of noise with long-range temporal correlations.