Abstract
We consider a stochastic differential equation with a quadratic nonlinearity in the noise. We derive equations for the steady state probability density and joint probability distribution valid beyond a markovian approximation. We do not assume that the strength of the random term is small. The equations are derived for the case of an Ornstein-Uhlenbeck noise and also for a dichotomic noise. A comparison is made. We discuss some examples for which correlation functions and the associated relaxation times are calculated.
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Sagués, F., San Miguel, M. & Sancho, J.M. Nonmarkovian dynamics of stochastic differential equations with quadratic noise. Z. Physik B - Condensed Matter 55, 269–282 (1984). https://doi.org/10.1007/BF01329022
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DOI: https://doi.org/10.1007/BF01329022