Related papers: Proximal Recursion for Solving the Fokker-Planck E…
The Fokker-Planck (FP) equation has been derived for describing the temporal evolution of the particle size probability density function (PDF) for KJMA (Kolmogorov-Johnson-Mehl-Avrami) transformations. The classical case of transformations…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
This paper presents a new type of Gronwall-Bellman inequality, which arises from a class of integral equations with a mixture of nonsingular and singular integrals. The new idea is to use a binomial function to combine the known…
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can…
We introduce a deep neural network-based numerical method for solving kinetic Fokker Planck equations, including both linear and nonlinear cases. Building upon the conservative dissipative structure of Vlasov-type equations, we formulate a…
In this paper, we propose a novel method to approximate the mean field stochastic differential equation by means of approximating the density function via Fokker-Planck equation. We construct a well-posed truncated Fokker-Planck equation…
We design the first parallel scheme based on Schwarz waveform relaxation methods for the Kolmogorov-Fokker-Planck equation. We introduce a new convergence proof for the algorithms. We also provide results about the existence and uniqueness…
While the nondegenerate case is well-known, there are only few results on the existence of strong solutions to McKean-Vlasov SDEs with coefficients of Nemytskii-type in the degenerate case. We consider a broad class of degenerate nonlinear…
We establish convergence rates for a fully discrete, multi-level, linear collocation method solving parametric elliptic PDEs on bounded polygonal domains with log-normal inputs. The method uses a finite set of function evaluations in the…
In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation…
Recently, the fractional Fokker-Planck equations (FFPEs) with multiple internal states are built for the particles undergoing anomalous diffusion with different waiting time distributions for different internal states, which describe the…
We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large $|x|$ using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does…
This work is devoted to studying complex dynamical systems under non-Gaussian fluctuations. We first estimate the Kantorovich-Rubinstein distance for solutions of non-local Fokker-Planck equations associated with stochastic differential…
The time evolution of probability densities for solutions to stochastic differential equations (SDEs) without delay is usually described by Fokker-Planck equations, which require the adjoint of the infinitesimal generator for the solutions.…
We propose a new stabilised finite element method for the classical Kolmogorov equation. The latter serves as a basic model problem for large classes of kinetic-type equations and, crucially, is characterised by degenerate diffusion. The…
The Fokker-Planck equation describing the transport of energetic particles interacting with turbulence is difficult to solve analytically. Numerical solutions are of course possible but they are not always useful for applications. In the…
Calibration of stochastic local volatility (SLV) models to their underlying local volatility model is often performed by numerically solving a two-dimensional non-linear forward Kolmogorov equation. We propose a novel finite volume (FV)…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
The continuous-discrete filtering problem requires the solution of a partial differential equation known as the Fokker-Planck-Kolmogorov forward equation (FPKfe). In this paper, it is pointed out that for a state model with an affine,…
We investigate the regularity of the law of Wong-Zakai-type approximations for It\^o stochastic differential equations. These approximations solve random differential equations where the diffusion coefficient is Wick-multiplied by the…