# Fokker-Planck Equation

@inproceedings{Risken1984FokkerPlanckE, title={Fokker-Planck Equation}, author={Hannes Risken}, year={1984} }

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 Langevin 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…

## 4,305 Citations

### A PERTURBATIVE APPROACH TO A CLASS OF FOKKER–PLANCK EQUATIONS

- Physics, Mathematics
- 2008

In this paper, we present a direct perturbative method to solving certain Fokker–Planck equations, which have constant diffusion coefficients and some small parameters in the drift coefficients. The…

### Microscopic dynamics of nonlinear Fokker-Planck equations.

- PhysicsPhysical review. E
- 2021

An approach to describe the effective microscopic dynamics of (power-law) nonlinear Fokker-Planck equations using a nonextensive generalization of the Wiener process to model thermal noise in electric circuits is proposed.

### Deriving fractional Fokker-Planck equations from a generalised master equation

- Physics
- 1999

A generalised master equation is constructed from a non-homogeneous random walk scheme. It is shown how fractional Fokker-Planck equations for the description of anomalous diffusion in external…

### A General Solution of the Fokker-Planck Equation

- Physics
- 2012

The Fokker-Planck equation is useful to describe stochastic processes. Depending on the force acting in the system, the solution of this equation becomes complicated and approximate or numerical…

### Exact solution of the Fokker-Planck equation for a broad class of diffusion coefficients.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

The asymptotic shape of the random-walk model and power-law decay obtained from other approaches can be reproduced from the solutions of the Langevin equation, by employing two simple functions for g (x,t) .

### Fluctuation theorem and an extended Fokker-Planck equation

- Physics
- 2005

Fluctuation in entropy production in stochastic dynamics is considered based on a Langevin equation. Starting from the path integral expression for the distribution function of the entropy production…

### Maximum Path Information and Fokker--Planck Equation

- Physics
- 2008

We present a rigorous method to derive the nonlinear Fokker–Planck (FP) equation of anomalous diffusion directly from a generalization of the principle of least action of Maupertuis proposed by Wang…

### Brownian Motion, Equations of Motion, and the Fokker-Planck Equations

- Physics
- 2002

The chapters which follow deal with nonequilibrium processes. First, in chapter 8, we treat the topic of the Langevin equations and the related Fokker-Planck equations. In the next chapter, the…

### A general nonlinear Fokker-Planck equation and its associated entropy

- Physics
- 2007

Abstract.A recently introduced nonlinear Fokker-Planck equation, derived
directly from a master equation, comes out as a very
general tool to describe phenomenologically systems presenting complex…

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