Stratonovich model driven by dichotomous noise: analytical results

Stationary and dynamic properties of the Stratonovich model driven by a dichotomous Markovian process (DMP) are investigated analytically. The stationary probability densityp_st and its moments are calculated exactly and the shape ofp_st is discussed in the whole parameter region. The location of the maxima ofp_st shows a behaviour similar to order parameters in continuous phase transitions. The time dependence of moments and the probability density is studied investigating (i) a series expansion of the formal solution for a given realization of the driving process, and (ii) the analytic behaviour of the Laplace transform of the probability density. As a function of physical parameters, qualitative changes of the long time behaviour may occur. Method (i) is generalized to determine the dynamics of moments for a superposition of independent DMP's (pregaussian noise).