Related papers: Exact simulation of the first-passage time of diff…

This paper provides an elementary, self-contained analysis of diffusion-based sampling methods for generative modeling. In contrast to existing approaches that rely on continuous-time processes and then discretize, our treatment works…

The aim of this paper is to study the law of the last passage time of a linear diffusion to a curved boundary. We start by giving a general expression for the density of such a random variable under some regularity assumptions. Following…

We extend the ideas of (Barbour 1990) and use Stein's method to obtain a bound on the distance between a scaled time-changed random walk and a time-changed Brownian Motion. We then apply this result to bound the distance between a…

Diffusion with an incorporated resetting mechanism provides a reference framework for modeling a wide range of natural phenomena. Within this framework, the optimal resetting rate is a key quantity that arises from the optimization of the…

We state an exact simulation scheme for the first passage time of a Brownian motion to a symmetric linear boundary.

We study the first-passage-time (FPT) properties of active Brownian particles to reach an absorbing wall in two dimensions. Employing a perturbation approach we obtain exact analytical predictions for the survival and FPT distributions for…

This letter introduces a formalism for modeling time-variant channels for diffusive molecular communication systems. In particular, we consider a fluid environment where one transmitter nano-machine and one receiver nano-machine are…

We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…

Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…

We introduce a unified framework for solving first passage times of time-homogeneous diffusion processes. According to the killed version potential theory and the perturbation theory, we are able to deduce closed-form solutions for…

The Inverse First Passage time problem seeks to determine the boundary corresponding to a given stochastic process and a fixed first passage time distribution. Here, we determine the numerical solution of this problem in the case of a two…

We study experimentally and theoretically the optimal mean time needed by a free diffusing Brownian particle to reach a target at a distance L from an initial position in the presence of resetting. Both the initial position and the…

While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…

Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widepsread. This deviation from brownian motion is usually characterized by a sublinear time dependence of the mean…

Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…

Diffusion models have become the go-to method for many generative tasks, particularly for image-to-image generation tasks such as super-resolution and inpainting. Current diffusion-based methods do not provide statistical guarantees…

Quantifying how spatial disorder affects the movement of a diffusing particle or agent is fundamental to target search studies. When diffusion occurs on a network, that is on a highly disordered environment, we lack the mathematical tools…

For three constrained Brownian motions, the excursion, the meander, and the reflected bridge, the densities of the maximum and of the time to reach it were expressed as double series by Majumdar, Randon-Furling, Kearney, and Yor (2008).…

We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…

We compare the relation between dispersion and dissipation for two random variables that can be used to characterize the precision of a Brownian clock. The first random variable is the current between states. In this case, a certain…