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A two-dimensional Fokker-Planck equation degenerating on a straight line

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Abstract

By an example of a two-dimensional hydrodynamic system, second-order Langevin equations with two correlated noise sources are investigated. It is shown that the asymptotic expression (t→∞) for the stationary distribution functionP depends on the order in which the limiting transitions;t→∞ andN 22→0 (N 22 is the power of one of the noises) are made. Using the method of local expansions in trigonometric form, approximate expressions are written for the distribution functionP at small but finiteN 22 tending atN 22→0 to the known exact solution.

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Authors and Affiliations

  1. Institute of Physics, BSSR Academy of Sciences, 220602, Minsk, USSR

    I. I. Fedchenia

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  1. I. I. Fedchenia
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Fedchenia, I.I. A two-dimensional Fokker-Planck equation degenerating on a straight line. J Stat Phys 52, 1005–1029 (1988). https://doi.org/10.1007/BF01019737

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  • DOI: https://doi.org/10.1007/BF01019737

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