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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

Stationary Distribution Asymptotic Approximation Planck Equation Left Boundary Exit Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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