Relaxation dynamics in the presence of pulse multiplicative noise sources with different correlation properties

The relaxation dynamics of a system described by a Langevin equation with pulse multiplicative noise sources with different correlation properties is considered. The solution of the corresponding Fokker-Planck equation is derived for Gaussian white noise. Moreover, two pulse processes with regulated periodicity are considered as a noise source: the dead-time-distorted Poisson process and the process with fixed time intervals, which is characterized by an infinite correlation time. We find that the steady state of the system is dependent on the correlation properties of the pulse noise. An increase of the noise correlation causes the decrease of the mean value of the solution at the steady state. The analytical results are in good agreement with the numerical ones.