Abstract The method of choice for integrating the time-dependent Fokker-Planck
equation in high-dimension is to generate samples from solution via
integration associated stochastic differential equation. Here, we study
an alternative scheme based on an ordinary equation
that describes flow probability. Acting as a transport map, this
equation deterministi...

We consider the kinetic Fokker–Planck equation with a class of general force. prove existence and uniqueness positive normalized equilibrium (in case force) establish some exponential rate convergence to (and can be explicitly computed). Our results improve about classical force case. result also improves for Fitzhugh–Nagumo from non-quantitative quantitative explicit rate.

We investigate variational methods for finding approximate solutions to the Fokker-Planck equation, especially in cases lacking detailed balance. These schemes fall into two classes: those in which a Hermitian operator is constructed from the (non-Hermitian) Fokker-Planck operator, and those which are based on soluble approximations to this operator. The various approaches are first tested on a...

The normalization condition, average values, and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A fractional (power) system is described by the fractional powers of coordinates and momenta. These systems can be considered as non-Hamiltonian systems in the usu...

The present note establishes the self-averaging, radiative transfer limit for the twofrequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The limiting equation is used to estimate thr...