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I Derivation of the Fokker-Planck Equation by Continuity

  1. Dec 23, 2016 #1
    Derive the Fokker-Planck equation by requiring conservation of probability:
    ∂VJ⋅dS=-d/dt∫Vp(r,t)dV
    The flux can be written as a sum of convective and diffusive terms
    J=p(r,t)v(r,t)-D(r,t)p(r,t)
    and substitution of this with use of the divergence theorem yields
    tp(x,t)=-∂x[p(x,t)v(x,t)]+∂x[D(x,t)∂xp(x,t)]
    where I have moved to one dimension for simplicity.

    However the form found here
    https://en.wikipedia.org/wiki/Fokker–Planck_equation
    is given as
    tp(x,t)=-∂x[p(x,t)v(x,t)]+∂x2[D(x,t)p(x,t)]

    I was wondering if anybody would be able to help me account for this difference. Thanks!
     
  2. jcsd
  3. Dec 23, 2016 #2

    mathman

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    Science Advisor
    Gold Member

    You might have better luck in a math forum.
     
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