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Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle…
Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…
In this paper we analyze fractional Fokker-Planck equation describing subdiffusion in the general infinitely divisible (ID) setting. We show that in the case of space-time-dependent drift and diffusion and time-dependent jump coefficient,…
In this article, we study the nonlinear Fokker-Planck (FP) equation that arises as a mean-field (macroscopic) approximation of bounded confidence opinion dynamics, where opinions are influenced by environmental noises and opinions of…
Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and play an important role in quantifying propagation and evolution of uncertainty. Although Fokker-Planck equations can be written…
We improve the standard theory of collisional stellar systems by considering the presence of a continuous mass distribution. The calculus of the diffusion coefficients is generalized and a new expression of the Fokker-Planck equation is…
We derive the steady state solution of the Fokker-Planck equation that describes the dynamics of the nondegenerate optical parametric oscillator in the truncated Wigner representation of the density operator. We assume that the pump mode is…
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…
Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion…
This work is devoted to the study of the Fokker--Planck equation for a stochastic heat equation with an additive $Q$-Wiener noise and non-homogeneous boundary conditions. We explicitly construct the probability density function and…
We address the problem of uncertainty propagation in the discrete Fourier transform by modeling the fast Fourier transform as a factor graph. Building on this representation, we propose an efficient framework for approximate Bayesian…
Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, severely limiting…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
Smoothed Particle Hydrodynamics (SPH_ is a mesh-free Lagrangian method renowned for modeling large deformations and free-surface flows, yet classical formulations remain confined to deterministic systems. We introduce Stochastic SPH…
Under low-collisionality conditions the isotropic part of the electron velocity distribution function in a plasma becomes non-local and the electrons can be described by a single global distribution function . This is also the regime…
We study a deterministic method for particle transport in tissue in selected medical applications. Generalized Fokker-Planck (GFP) theory has been developed to improve the Fokker-Planck (FP) equation in cases where scattering is…
The Fokker-Planck equation (FPE) is the partial differential equation that governs the density evolution of the It\^o process and is of great importance to the literature of statistical physics and machine learning. The FPE can be regarded…
Universal difference quotient representations are introduced for the exact self-sameness principles (SSP) as rules for rates of change introduced in [Clemence-Mkhope, D.P (2021, Preprint). The Exact Spectral Derivative Discretization Finite…
The Fokker-Planck (FP) equation governs the evolution of densities for stochastic dynamics of physical systems, such as the Langevin dynamics and the Lorenz system. This work simulates FP equations through a mean field control (MFC)…
Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction…