Related papers: A stochastic diffusion process for Lochner's gener…
The method of potential solutions of Fokker-Planck equations is used to develop a transport equation for the joint probability of N coupled stochastic variables with the Dirichlet distribution as its asymptotic solution. To ensure a bounded…
We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be…
In this work, we present a theoretical and computational framework for constructing stochastic transport maps between probability distributions using diffusion processes. We begin by proving that the time-marginal distribution of the sum of…
We consider a continuous random walk model for describing normal as well as anomalous diffusion of particles subjected to an external force when these particles diffuse in a uniformly expanding (or contracting) medium. A general equation…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
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…
Approximate weak solutions of the Fokker-Planck equation can represent a useful tool to analyze the equilibrium fluctuations of birth-death systems, as they provide a quantitative knowledge lying in between numerical simulations and exact…
The~numerical solutions to a non-linear Fractional Fokker--Planck (FFP) equation are studied estimating the generalized diffusion coefficients. The~aim is to model anomalous diffusion using an FFP description with fractional velocity…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, It\^o diffusive process is generalized by incorporating a multiplicative noise term…
Employing time-dependent projection formalism, a Fokker-Planck equation with non-Markovian transport coefficients is derived for large amplitude collective motion. Properties of transport coefficients for diffusion processes in a potential…
A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…
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…
Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…
We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution,…
The influence of crowding on the diffusion of tagged particles in a dense medium is investigated in the framework of a mean-field model, derived in the continuum limit from a microscopic stochastic process with exclusion. The probability…
The Fokker-Planck equation is a partial differential equation that describes the evolution of a probability distribution over time. It is used to model a wide range of physical and biological phenomena, such as diffusion, chemical…
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we study an alternative…
Mathematical models based on probability density functions (PDF) have been extensively used in hydrology and subsurface flow problems, to describe the uncertainty in porous media properties (e.g., permeability modelled as random field).…
We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter…