Benjamin Arras
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View article: Some Notes on Quantitative Generalized CLTs with Self-Decomposable Limiting Laws by Spectral Methods
Some Notes on Quantitative Generalized CLTs with Self-Decomposable Limiting Laws by Spectral Methods Open
In these notes, we obtain new stability estimates for centered non-degenerate selfdecomposable probability measures on $\mathbb{R}^d$ with finite second moment and for non-degenerate symmetric $α$-stable probability measures on $\mathbb{R}…
View article: Covariance Representations, $L^p$-Poincaré Inequalities, Stein's Kernels and High Dimensional CLTs
Covariance Representations, $L^p$-Poincaré Inequalities, Stein's Kernels and High Dimensional CLTs Open
We explore connections between covariance representations, Bismut-type formulas and Stein's method. First, using the theory of closed symmetric forms, we derive covariance representations for several well-known probability measures on $\ma…
View article: On Some Operators Associated with Non-Degenerate Symmetric $\alpha$-Stable Probability Measures.
On Some Operators Associated with Non-Degenerate Symmetric $\alpha$-Stable Probability Measures. Open
Boundedness properties of operators associated with non-degenerate symmetric $\alpha$-stable, $\alpha \in (1,2)$, probability measures on $\mathbb{R}^d$ are investigated on appropriate, Euclidean or otherwise, $L^p$-spaces, $p \in (1,+\inf…
View article: Dimension Free Estimates for the Riesz Transforms Associated with some Fractional Operators
Dimension Free Estimates for the Riesz Transforms Associated with some Fractional Operators Open
In these notes, boundedness properties of the Riesz transforms associated with symmetric $\alpha$-stable probability measures, $\alpha \in (1,2)$, are investigated on appropriate $L^p$ spaces, for $p \in (1,+\infty)$. Our approach is based…
View article: Stein characterizations for linear combinations of gamma random variables
Stein characterizations for linear combinations of gamma random variables Open
In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply this to study random variables which can be represented as…
View article: Some recent advances for limit theorems
Some recent advances for limit theorems Open
We present some recent developments for limit theorems in probability theory, illustrating the variety of this field of activity. The recent results we discuss range from Stein’s method, as well as for infinitely divisible distributions as…
View article: Sequential Sampling for Optimal Weighted Least Squares Approximations in Hierarchical Spaces
Sequential Sampling for Optimal Weighted Least Squares Approximations in Hierarchical Spaces Open
We consider the problem of approximating an unknown function $u\in L^2(D,ρ)$ from its evaluations at given sampling points $x^1,\dots,x^n\in D$, where $D\subset \mathbb{R}^d$ is a general domain and $ρ$ is a probability measure. The approx…
View article: Quantifying Early-Age Concrete Mechanical Properties and Curing Conditions Utilizing an Automated System
Quantifying Early-Age Concrete Mechanical Properties and Curing Conditions Utilizing an Automated System Open
The validation of concrete quality based on the 28-day strength is a lengthy process. Predicting concrete mechanical properties through early-age methods can streamline the construction process. Early-age concrete behavior consists of asse…
View article: On Stein’s method for multivariate self-decomposable laws
On Stein’s method for multivariate self-decomposable laws Open
This work explores and develops elements of Stein’s method of approximation in the infinitely divisible setting, and its connections to functional analysis. It is mainly concerned with multivariate self-decomposable laws without finite fir…
View article: IT Formulae for Gamma Target: Mutual Information and Relative Entropy
IT Formulae for Gamma Target: Mutual Information and Relative Entropy Open
In this paper, we introduce new Stein identities for gamma target\ndistribution as well as a new non-linear channel specifically designed for\ngamma inputs. From these two ingredients, we derive an explicit and simple\nformula for the deri…
View article: Stein characterizations for linear combinations of gamma random variables
Stein characterizations for linear combinations of gamma random variables Open
In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply this to study random variables which can be represented as…
View article: Stein characterizations for linear combinations of gamma random\n variables
Stein characterizations for linear combinations of gamma random\n variables Open
In this paper we propose a new, simple and explicit mechanism allowing to\nderive Stein operators for random variables whose characteristic function\nsatisfies a simple ODE. We apply this to study random variables which can be\nrepresented…
View article: A bound on the 2-Wasserstein distance between linear combinations of independent random variables
A bound on the 2-Wasserstein distance between linear combinations of independent random variables Open
We provide a bound on a natural distance between finitely and infinitely supported elements of the unit sphere of $\ell^2(\mathbb{N}^*)$, the space of real valued sequences with finite $\ell^2$ norm. We use this bound to estimate the 2-Was…
View article: From forward integrals to Wick-Itô integrals: the fractional Brownian motion and the Rosenblatt process cases
From forward integrals to Wick-Itô integrals: the fractional Brownian motion and the Rosenblatt process cases Open
In this paper, we combine Hida distribution theory and Sobolev-Watanabe-Kree spaces in order to study finely the link between forward integrals obtained by regularization and Wick-Itô integrals with respect to fractional Brownian motion an…
View article: A new approach to the Stein-Tikhomirov method: with applications to the\n second Wiener chaos and Dickman convergence
A new approach to the Stein-Tikhomirov method: with applications to the\n second Wiener chaos and Dickman convergence Open
In this paper, we propose a general means of estimating the rate at which\nconvergences in law occur. Our approach, which is an extension of the classical\nStein-Tikhomirov method, rests on a new pair of linear operators acting on\ncharact…
View article: A new approach to the Stein-Tikhomirov method: with applications to the second Wiener chaos and Dickman convergence
A new approach to the Stein-Tikhomirov method: with applications to the second Wiener chaos and Dickman convergence Open
In this paper, we propose a general means of estimating the rate at which convergences in law occur. Our approach, which is an extension of the classical Stein-Tikhomirov method, rests on a new pair of linear operators acting on characteri…
View article: Stein's method on the second Wiener chaos : 2-Wasserstein distance
Stein's method on the second Wiener chaos : 2-Wasserstein distance Open
In the first part of the paper we use a new Fourier technique to obtain a Stein characterizations for random variables in the second Wiener chaos. We provide the connection between this result and similar conclusions that can be derived us…