Stochastic equations of the Langevin type under a weakly dependent perturbation |
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Authors: | Roman V Bobryk |
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Institution: | (1) Institute for Applied Problems of Mechanics and Mathematics of Ukrainian Academy of Sciences, Naukova 3-b, Lviv, Ukraine |
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Abstract: | Asymptotic expansions for the probability density of the solution of a stochastic differential equation under a weakly dependent perturbation are proposed. In particular, linear partial differential equations for the first two terms of the correlation time expansion are derived. It is shown that in these expansions the boundary layer part appears and non-Gaussianity of the perturbation is important for the Fokker-Planck approximation correction. |
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Keywords: | Langevin equation stochastic Liouville equation Fokker-Planck equation correlation time expansion |
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