Relationship between a Non-Markovian Process and Fokker-Planck Equation

Details Relationship between a Non-Markovian Process and Fokker-Planck Equation Relationship between a Non-Markovian Process and Fokker-Planck Equation

2006-03-09

arxiv.org/abs/cond-mat/0603252v2

Physics

Condensed Matter

Statistical Mechanics

14 pages, 17 figures

Scientific paper

10.1016/j.physleta.2006.06.063

We demonstrate the equivalence of a Non--Markovian evolution equation with a linear memory--coupling and a Fokker--Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to an initial distribution, the corresponding FPE offers a non-trivial drift term depending itself on the diffusion parameter. As the consequence the deterministic part of the underlying Langevin equation is likewise determined by the noise strength of the stochastic part. This memory induced stochastic behavior is discussed for different initial distributions. The analytical calculations are supported by numerical results.

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