Stochastic system with colored correlation between white noise and colored noise

A stochastic system with colored correlation between white noise and colored noise is investigated theoretically. A general Fokker–Planck equation of the system is derived by using a standard method. We discuss a bistable system with colored correlation between additive white noise and multiplicative colored one. It is found that the effects of the correlation time of multiplicative colored noise on the statistical properties of the bistable system are different from those of the correlation time of the correlation between additive white noise and multiplicative colored noise on the statistical properties of the bistable system.