English
Related papers

Related papers: Concentration analysis of multivariate elliptic di…

200 papers

We construct admissible circulant Laplacian matrix functions as generators for strictly increasing random walks on the integer line. These Laplacian matrix functions refer to a certain class of Bernstein functions. The approach has…

Probability · Mathematics 2020-12-10 Thomas M. Michelitsch , Federico Polito , Alejandro P. Riascos

Basic derivative formulas are presented for hypoelliptic heat semigroups and harmonic functions extending earlier work in the elliptic case. Emphasis is placed on developing integration by parts formulas at the level of local martingales.…

Probability · Mathematics 2010-05-02 Marc Arnaudon , Anton Thalmaier

Stochastic processes play a key role for modeling a huge variety of transport problems out of equilibrium, with manifold applications throughout the natural and social sciences. To formulate models of stochastic dynamics the conventional…

Statistical Mechanics · Physics 2022-07-25 Massimiliano Giona , Andrea Cairoli , Rainer Klages

We consider the problem of regression learning for deterministic design and independent random errors. We start by proving a sharp PAC-Bayesian type bound for the exponentially weighted aggregate (EWA) under the expected squared empirical…

Applications · Statistics 2012-06-27 Arnak Dalalyan , Alexandre B. Tsybakov

We show the relation between processes which are modeled by a Langevin equation with multiplicative noise and infinite ergodic theory. We concentrate on a spatially dependent diffusion coefficient that behaves as ${D(x)}\sim…

Statistical Mechanics · Physics 2019-05-01 N. Leibovich , E. Barkai

We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…

Probability · Mathematics 2020-09-23 Grégoire Ferré , Gabriel Stoltz

We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. We assume that the intensity of each Poisson process is of the form $s (\cdot, x)$ where $x$ is the covariate and where $s$ is an…

Statistics Theory · Mathematics 2013-06-14 Mathieu Sart

We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…

Number Theory · Mathematics 2025-12-03 Victor Bernal Ramirez , Arturo Jaramillo

Diffusion models have emerged as powerful tools for solving inverse problems, yet prior work has primarily focused on observations with Gaussian measurement noise, restricting their use in real-world scenarios. This limitation persists due…

Machine Learning · Statistics 2025-02-11 Alessandro Micheli , Mélodie Monod , Samir Bhatt

This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which…

Optimization and Control · Mathematics 2024-05-27 Angeliki Kamoutsi , Peter Schmitt-Förster , Tobias Sutter , Volkan Cevher , John Lygeros

In this work, we study the problem of aggregating a finite number of predictors for nonstationary sub-linear processes. We provide oracle inequalities relying essentially on three ingredients: (1) a uniform bound of the $\ell^1$ norm of the…

Statistics Theory · Mathematics 2015-11-18 Christophe Giraud , François Roueff , Andres Sanchez-Perez

We prove that probability laws of certain multidimensional semimartingales which includes time-inhomogenous diffusions, under suitable assumptions, satisfy Quadratic Transportation Cost Inequality under the uniform metric. From this we…

Probability · Mathematics 2011-04-22 Soumik Pal

Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…

Analysis of PDEs · Mathematics 2024-04-05 Katy Craig , Matt Jacobs , Olga Turanova

Up to now, the nonparametric analysis of multidimensional continuous-time Markov processes has focussed strongly on specific model choices, mostly related to symmetry of the semigroup. While this approach allows to study the performance of…

Statistics Theory · Mathematics 2022-11-04 Niklas Dexheimer , Claudia Strauch , Lukas Trottner

A canonical algorithm for log-concave sampling is the Langevin Algorithm, aka the Langevin Diffusion run with some discretization stepsize $\eta > 0$. This discretization leads the Langevin Algorithm to have a stationary distribution…

Machine Learning · Statistics 2024-10-22 Jason M. Altschuler , Kunal Talwar

This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…

Statistics Theory · Mathematics 2010-08-18 Jimmy Olsson , Jonas Ströjby

We prove several different anti-concentration inequalities for functions of independent Bernoulli-distributed random variables. First, motivated by a conjecture of Alon, Hefetz, Krivelevich and Tyomkyn, we prove some "Poisson-type"…

Combinatorics · Mathematics 2023-06-22 Jacob Fox , Matthew Kwan , Lisa Sauermann

This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target…

Methodology · Statistics 2018-12-07 Andi Q. Wang , Martin Kolb , Gareth O. Roberts , David Steinsaltz

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…

Probability · Mathematics 2007-05-23 Liqun Wang , Klaus Pötzelberger

This paper proposes a new methodology to perform Bayesian inference for a class of multidimensional Cox processes in which the intensity function is piecewise constant. Poisson processes with piecewise constant intensity functions are…

Methodology · Statistics 2022-11-16 Flavio B. Gonçalves , Barbara C. C. Dias