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The authors present a method of indicator random processes, applicable to constructing models of jump processes associated with diffusion process. Indicator random processes are processes that take only two values: 1 and 0, in accordance…
We analyse deterministic diffusion in a simple, one-dimensional setting consisting of a family of four parameter dependent, chaotic maps defined over the real line. When iterated under these maps, a probability density function spreads out…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
The purpose of this paper is to provide new formulas for the estimation of the effective diffusion coefficient of an equation of Fick-Jacob's type obtained by projecting the two-dimensional diffusion equation along the normal direction of…
We present a general scheme to calculate within the independent interval approximation generalized (level-dependent) persistence properties for processes having a finite density of zero-crossings. Our results are especially relevant for the…
These are lecture notes for various Summer and Winter schools that I have given. The notes describe the methodology called Variational Modelling, and focus on the application to the modelling of gradient-flow systems. I describe the…
This work studies the parameter-dependent diffusion equation in a two-dimensional domain consisting of locally mirror symmetric layers. It is assumed that the diffusion coefficient is a constant in each layer. The goal is to find…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly…
In this paper we present a novel inference methodology to perform Bayesian inference for spatiotemporal Cox processes where the intensity function depends on a multivariate Gaussian process. Dynamic Gaussian processes are introduced to…
Based on Fick's 2nd law the development of moving particle semi-implicit method for predicting diffusion process is proposed in this study
The presented explanations are provided for the one--dimensional diffusion process with constant drift by using forward Fokker--Planck technique. We are interested in the outflow probability in a finite interval, i.e. first passage time…
A particle driven by deterministic chaos and moving in a spatially extended environment can exhibit normal diffusion, with its mean square displacement growing proportional to the time. Here we consider the dependence of the diffusion…
Score-based diffusion models have proven effective in image generation and have gained widespread usage; however, the underlying factors contributing to the performance disparity between stochastic and deterministic (i.e., the probability…
Methods that rely on proxies, without imposing strong parametric structure, are increasingly used to deal with unobserved variables in causal inference. One influential line of this work reconstructs latent distributions used to identify…
In a functional setting, we propose two test statistics to highlight the Poisson nature of a Cox process when n copies of the process are available. Our approach involves a comparison of the empirical mean and the empirical variance of the…
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…
The paper studies a higher-order diffusion model of Maxwell-Stefan kind. The model is based upon higher-order moment equations of kinetic theory of mixtures, which include viscous dissipation in the model. Governing equations are analyzed…
The problem of diffusion in a porous medium with a spatially varying porosity is considered. The particular microstructure analyzed comprises a collection of impenetrable spheres, though the methods developed are general. Two different…