Abstract
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).
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Teubel, A., Behn, U. & Kühnel, A. Stratonovich model driven by dichotomous noise: analytical results. Z. Physik B - Condensed Matter 71, 393–402 (1988). https://doi.org/10.1007/BF01312499
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DOI: https://doi.org/10.1007/BF01312499