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Fokker-Planck Equation

1984; Springer Nature; Linguagem: Inglês

10.1007/978-3-642-96807-5_4

2198-333X

Hannes Risken,

Statistical Mechanics and Entropy

As shown in Sects. 3.1, 2 we can immediately obtain expectation values for processes described by the linear Langevin equations (3.1, 31). For nonlinear Lange vin equations (3.67, 110) expectation values are much more difficult to obtain, so here we first try to derive an equation for the distribution function. As mentioned already in the introduction, a differential equation for the distribution function describing Brownian motion was first derived by Fokker [1.1] and Planck [1.2]: many review articles and books on the Fokker-Planck equation now exist [1.5–15].