Related papers: Limit theorems for rarefaction of set of diffusion…

We present a central limit theorem for stationary random fields that are short-range dependent and asymptotically independent. As an application, we present a central limit theorem for an infinite family of interacting It\^o-type diffusion…

We study a finite system of diffusions on the half-line, absorbed when they hit zero, with a correlation effect that is controlled by the proportion of the processes that have been absorbed. As the number of processes in the system becomes…

This paper investigates a diffusion process in a narrow tubular domain with reflecting boundary conditions, where the geometry serves as a singular perturbation of an underlying graph in $\mathbb{R}^2$ or $\mathbb{R}^3$. The construction…

We consider the subdiffusion--absorption process in a system which consists of two different media separated by a thin membrane. The process is described by subdiffusion--absorption equations with fractional Riemann--Liouville time…

The study of discrete-time stochastic processes on the half-line with mean drift at $x$ given by $\mu_1 (x) \to 0$ as $x \to \infty$ is known as Lamperti's problem. We give sharp almost-sure bounds for processes of this type in the case…

We consider an infinite system of quasilinear first-order partial differential equations, generalized to contain spacial integration, which describes an incompressible fluid mixture of infinite components in a line segment whose motion is…

Different approaches are presented to investigate diffusion from a point source in a slab delimited by two absorbing boundaries consisting of parallel infinite planes. These approaches enable to consider the effect of absorption at the…

We introduce a new diffusion process which arises as the $n\to\infty$ limit of a Bessel process of dimension $d \ge 2$ conditioned upon remaining bounded below one until time $n$. In addition to being interesting in its own right, we argue…

We establish the zero-diffusion limit for both continuous and discrete aggregation models over convex and bounded domains. Compared with a similar zero-diffusion limit derived in [44], our approach is different and relies on a coupling…

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative…

A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…

We identify the integrable stopping time $\tau_*$ with minimal $L^1$-distance to the last-passage time $\gamma_z$ to a given level $z>0$, for an arbitrary non-negative time-homogeneous transient diffusion $X$. We demonstrate that $\tau_*$…

We assume that we observe $N$ independent copies of a diffusion process on a time-interval $[0,2T]$. For a given time $t$, we estimate the transition density $p_t(x,y)$, namely the conditional density of $X_{t + s}$ given $X_s = x$, under…

Diffusion processes have been widely used for approximations in the queueing theory. There are different types of diffusion approximations. Among them, we are interested in those obtained through limits of a sequence of models which…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…

The probability density is a fundamental quantity for characterizing diffusion processes. However, it is seldom known except in a few renowned cases, including Brownian motion and the Ornstein-Uhlenbeck process and their bridges, geometric…

Let $M$ be a compact connected Riemannian manifold possibly with a boundary, let $V\in C^2(M)$ such that $\mu(d x):=e^{V(x)}d x$ is a probability measure, and let $\{\lambda_i\}_{i\ge 1} $ be all non-trivial eigenvalues of $-L$ with Neumann…

We discuss an initial-boundary value problem for a fractional diffusion equation with Caputo time-fractional derivative where the coefficients are dependent on spatial and time variables and the zero Dirichlet boundary condition is…

This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…

We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of…