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Discussion of ``The Dantzig selector: Statistical estimation when $p$ is much larger than $n$'' [math/0506081]

Statistics Theory · Mathematics 2008-12-18 Ya'acov Ritov

In the present work, we explore homogenization techniques for a class of switching diffusion processes whose drift and diffusion coefficients, and jump intensities are smooth, spatially periodic functions; we assume full coupling between…

Probability · Mathematics 2025-07-01 Chetan D. Pahlajani

In this work, we consider the numerical recovery of a spatially dependent diffusion coefficient in a subdiffusion model from distributed observations. The subdiffusion model involves a Caputo fractional derivative of order $\alpha\in(0,1)$…

Numerical Analysis · Mathematics 2021-01-12 Bangti Jin , Zhi Zhou

It\^{o} processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such It\^{o} processes. We are interested in the…

Statistics Theory · Mathematics 2008-12-10 Per Aslak Mykland , Lan Zhang

For the case of approximation of convection--diffusion equations using piecewise affine continuous finite elements a new edge-based nonlinear diffusion operator is proposed that makes the scheme satisfy a discrete maximum principle. The…

Numerical Analysis · Mathematics 2015-09-30 Gabriel R. Barrenechea , Erik Burman , Fotini Karakatsani

Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…

Statistical Mechanics · Physics 2026-01-16 Gabriel Barreiro , Vladimir Pérez-Veloz

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…

Machine Learning · Computer Science 2023-05-02 Lequan Lin , Zhengkun Li , Ruikun Li , Xuliang Li , Junbin Gao

Two aspects of noncolliding diffusion processes have been extensively studied. One of them is the fact that they are realized as harmonic Doob transforms of absorbing particle systems in the Weyl chambers. Another aspect is integrability in…

Probability · Mathematics 2014-07-18 Makoto Katori

To estimate a sparse linear model from data with Gaussian noise, consilience from lasso and compressed sensing literatures is that thresholding estimators like lasso and the Dantzig selector have the ability in some situations to identify…

Machine Learning · Statistics 2017-08-14 Jairo Diaz-Rodriguez , Sylvain Sardy

Currently, there is no general theory for deriving diffusion approximations of queueing systems with high- or infinite-dimensional state descriptors. In this paper, we explore one path for deriving diffusion limit equations of queueing…

Probability · Mathematics 2026-05-28 Eva H Loeser

This paper is concerned with the study of a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. A main subject of interest is to understand how the presence of diffusion acts as a selection principle, which…

Analysis of PDEs · Mathematics 2016-01-27 Joseph G. Conlon , Michael Dabkowski , Jingchen Wu

In this paper we present a novel method for estimating the parameters of a parametric diffusion processes. Our approach is based on a closed-form Maximum Likelihood estimator for an approximating Continuous Time Markov Chain (CTMC) of the…

Methodology · Statistics 2021-08-31 J. L. Kirkby , Dang Nguyen , Duy Nguyen , Nhu Nguyen

Diffusion phenomena in a multiple component lattice Boltzmann Equation (LBE) model are discussed in detail. The mass fluxes associated with different mechanical driving forces are obtained using a Chapman-Enskog analysis. This model is…

comp-gas · Physics 2009-10-28 Xiaowen Shan , Gary Doolen

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

Computer Vision and Pattern Recognition · Computer Science 2026-01-28 Roberto Miele , Niklas Linde

In this paper we study the diffusion approximation of a swarming model given by a system of interacting Langevin equations with nonlinear friction. The diffusion approximation requires the calculation of the drift and diffusion coefficients…

Numerical Analysis · Mathematics 2015-05-08 V. Bonnaillie-Noël , J. A. Carrillo , T. Goudon , G. A. Pavliotis

The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is…

Statistics Theory · Mathematics 2024-01-31 Patricia Román-Román , Juan José Serrano-Pérez , Francisco Torres-Ruiz

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…

Statistics Theory · Mathematics 2020-09-14 Yaozhong Hu , Yuejuan Xi

In this work we derive a posteriori error estimates for the convection-diffusion-reaction equation coupled with the Darcy-Forchheimer problem by a nonlinear external source depending on the concentration of the fluid. We introduce the…

Numerical Analysis · Mathematics 2022-12-27 Toni Sayah , Georges Semaan , Faouzi Triki

Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs. Existing methods for diffusion models typically require access to model gradients or retraining, limiting their…

Machine Learning · Computer Science 2025-10-17 Yutian Zhao , Chao Du , Xiaosen Zheng , Tianyu Pang , Min Lin

There has been considerable recent study in "sub-diffusion" models that replace the standard parabolic equation model by a one with a fractional derivative in the time variable. There are many ways to look at this newer approach and one…

Analysis of PDEs · Mathematics 2019-04-08 William Rundell , Zhidong Zhang