Abstract. The object of this paper is the uniqueness for a d-dimensional Fokker-Planck type equation with non-homogeneous (possibly degenerated) measurable not necessarily bounded coefficients. We provide an application to the probabilistic representation of the so called Barenblatt solution of the fast diffusion equation which is the partial differential equation ∂tu = ∂ 2 xx u with m ∈ (0, 1)...

We derive the Fokker-Planck operator describing a highly forward peaked scattering process in the linear transport equation, in anisotropic media, as a formal asymptotic limit of the exact integral operator. The resulting operator, being both con-vective and diiusive in angle and energy variables, reduces the degenerate nature of the Fokker-Planck system compared to the isotropic media case whe...

We study, in axisymmetnc geometry, a discretization of the Fokker-Planck operator that preserves the physical properties which are decrease of the kinetic entropy and conservation of mass, momentum and energy and only those quantifies For this purpose, we exhibit how the above properties are conséquences, first, of the algebraic structure of the Landau form of the Fokker-Planck operator and, se...

3 The “Fokker-Planck” equation is a partial differential equation that controls the evolution of the forward (and backward) probabilities 9 3.1 Deriving the “free” Fokker-Planck equation (no spike observations) . . . . . . 10 3.1.1 Conductance-based model . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.2 Computing mean firing rates in a network of GLM neurons . . . . . . 13 3.2 Incorpo...

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—...

In this paper we discuss the relation between ensemble learning, deterministic annealing and Markov chain sample and optimization methods on the one hand and the Fokker-Planck Machine on the other hand. The latter was introduced as an alternative method for high-dimensional non-convex optimization, as often encountered in training of neural networks. We demonstrate how the Fokker-Planck Machine...

We derive simple formulas connecting the generalized Wigner functions for s-ordering with the density matrix, and vice-versa. These formulas proved very useful for quantum mechanical applications, as, for example, for connecting master equations with Fokker-Planck equations, or for evaluating the quantum state from Monte Carlo simulations of Fokker-Planck equations, and finally for studying pos...

This article is concerned with maximal accretive realization of geometric Kramers-Fokker-Planck operators on manifolds with boundaries. A general class of boundary conditions is introduced which ensures the maximal accretivity and some global subelliptic estimates. Those estimates imply nice spectral properties as well as exponential decay properties for the associated semigroup. Admissible bou...

On the basis of our Fokker-Planck code “FPI”, a new kernel for nonlocal electron transport in plasmas has been developed. Large scale simulations of plasma macroscopic characteristics have been made by using both this Fokker-Planck and a new Hydrodynamic code using the new kernel [1]. However, these simulations were made with the approximation of spherical Rosenbluth potentials. We have now add...