The Fokker—Planck Equation: One Dimension

  • Johan Grasman
  • Onno A. van Herwaarden
Part of the Springer Series in Synergetics book series (SSSYN)

Abstract

Let us consider a stochastic process described by the scalar X(t) with probability density p(t, x) satisfying
$$\frac{{\partial p}}{{\partial t}} = - \frac{\partial }{{\partial x}}(b(x)p) + \frac{{{\varepsilon ^2}}}{2}\frac{{{\partial ^2}}}{{\partial {x^2}}}(a(x)p) $$
(3.1a)
for 0 < x < 1 and t > 0
$$p(0,x) = {p_0}(x),\;\;\;\int\limits_0^1 {{p_0}(x)dx = 1.} $$
(3.1b)

Keywords

Rium 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Johan Grasman
    • 1
  • Onno A. van Herwaarden
    • 1
  1. 1.Department of MathematicsAgricultural UniversityWageningenThe Netherlands

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