Infinite dimensional Langevin equation and Fokker-Planck equation

The Fokker-Planck equation

In 1984, H. Risken authored a book (H. Risken, The Fokker-Planck Equation: Methods of Solution, Applications, Springer-Verlag, Berlin, New York) discussing the Fokker-Planck equation for one variable, several variables, methods of solution and its applications, especially dealing with laser statistics. There has been a considerable progress on the topic as well as the topic has received greater...

The Fokker-Planck Equation

Stochastic differential equations (SDE) are used to model many situations including population dynamics, protein kinetics, turbulence, finance, and engineering [5, 6, 1]. Knowing the solution of the SDE in question leads to interesting analysis of the trajectories. Most SDE are unsolvable analytically and other methods must be used to analyze properties of the stochastic process. From the SDE, ...

Fokker-Planck Equation

The Langevin equation approach to the evolution of the velocity distribution for the Brownian particle might leave you uncomfortable. A more formal treatment of this type of problem is given by the Fokker-Planck equation. We can either formulate the question in terms of the evolution of a nonstationary probability distribution from a defined initial condition, or in terms of the evolution of th...

Iterative methods for solving non linear Fokker-Planck equation

Fokker-Planck Equation and Thermodynamic System Analysis

The non-linear Fokker-Planck equation or Kolmogorov forward equation is currently successfully applied for deep analysis of irreversibility and it gives an excellent approximation near the free energy minimum, just as Boltzmann’s definition of entropy follows from finding the maximum entropy state. A connection to Fokker-Planck dynamics and the free energy functional is presented and discussed—...