Related papers: Discretized Diffusion Processes
This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator…
In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain $D$ of $ \mathbb{R}^{k}$, $k\ge 1$, which includes the fractional power $\mathcal L^\beta$, $0<\beta\le…
We give a very simple method for finding the exact analytical solution for the problem of a particle undergoing diffusive motion on a flat potential in the presence of a gaussian sink function. The diffusion process is modelled by using one…
A core challenge in Machine Learning is to learn to disentangle natural factors of variation in data (e.g. object shape vs. pose). A popular approach to disentanglement consists in learning to map each of these factors to distinct subspaces…
Information diffusion prediction is a fundamental task which forecasts how an information item will spread among users. In recent years, deep learning based methods, especially those based on recurrent neural networks (RNNs), have achieved…
We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic potential. We uncover the dependence of ensemble- and…
In this paper, we study four nonlocal diffusion operators, including the fractional Laplacian, spectral fractional Laplacian, regional fractional Laplacian, and peridynamic operator. These operators represent the infinitesimal generators of…
We consider the Laplacian in $\mathbb{R}^n$ perturbed by a finite number of distant perturbations those are abstract localized operators. We study the asymptotic behaviour of the discrete spectrum as the distances between perturbations tend…
We consider the spectral definition of the fractional Laplace operator and study a basic linear problem involving this operator and singular forcing. In two dimensions, we introduce an appropriate weak formulation in fractional Sobolev…
The Laplacian $\Delta$ is the infinitesimal generator of isotropic Brownian motion, being the limit process of normal diffusion, while the fractional Laplacian $\Delta^{\beta/2}$ serves as the infinitesimal generator of the limit process of…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms,…
The focus of this article is studying an optimal control problem for branching diffusion processes. Initially, we introduce the problem in its strong formulation and expand it to include linearly growing drifts. Then, we present a relaxed…
Stochastic reaction-diffusion models can be analytically studied on complex networks using the linear noise approximation. This is illustrated through the use of a specific stochastic model, which displays traveling waves in its…
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…
Distributed control increases system scalability, flexibility, and redundancy. Foundational to such decentralisation is consensus formation, by which decision-making and coordination are achieved. However, decentralised multi-agent systems…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…