Abstract
We consider stochastic differential equations of the Langevin type in which the noise enters nonlinearly. In particular we study quadratic gaussian noise and we derive equations for the probability density under different approximations. In the limit of small intensity and small correlation time of the noise we obtain a Fokker-Planck equation which accounts for the main effects of the nonlinear noise. We present some examples and we discuss the consequences of our results in the analysis of an electrohydrodynamic instability in liquid crystals in the presence of external noise.
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Miguel, M.S., Sancho, J.M. Theory of nonlinear Gaussian noise. Z. Physik B - Condensed Matter 43, 361–372 (1981). https://doi.org/10.1007/BF01292804
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DOI: https://doi.org/10.1007/BF01292804