Publications (18)
IT formulae for gamma target: mutual information and relative entropy
Benjamin Arras, Yvik Swan
In this paper, we introduce new Stein identities for gamma target distribution as well as a new non-linear channel specifically designed for gamma inputs. From these two ingredient…
From forward integrals to Wick-Itô integrals: the fractional Brownian motion and the Rosenblatt process cases
Benjamin Arras
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-…
On Stein's Method for Multivariate Self-Decomposable Laws With Finite First Moment
Benjamin Arras, Christian Houdré
We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in having finite first moment. Building on previous univariate fi…
A white noise approach to stochastic integration with respect to the Rosenblatt process
Benjamin Arras
In this paper, we define a stochastic calculus with respect to the Rosenblatt process by means of white noise distribution theory. For this purpose, we compute the translated chara…
Some Notes on Quantitative Generalized CLTs with Self-Decomposable Limiting Laws by Spectral Methods
Benjamin Arras
In these notes, we obtain new stability estimates for centered non-degenerate selfdecomposable probability measures on with finite second moment and for non-degenera…
On Some Operators Associated with Non-Degenerate Symmetric -Stable Probability Measures
Benjamin Arras, Christian Houdré
Boundedness properties of operators associated with non-degenerate symmetric -stable, , probability measures on are investigated on appropriate, Euc…
Around the Sobolev Inequalities for the Stable Heat Semigroups
Benjamin Arras, Christian Houdré
We develop a general distributional theory of fractional (an)isotropic Sobolev spaces associated with the non-degenerate symmetric -stable, , probability measures…
From almost sure local regularity to almost sure Hausdorff dimension for Gaussian fields
Erick Herbin, Benjamin Arras, Geoffroy Barruel
Fine regularity of stochastic processes is usually measured in a local way by local Hölder exponents and in a global way by fractal dimensions. Following a previous work of Adler,…
Covariance Representations, -Poincaré Inequalities, Stein's Kernels and High Dimensional CLTs
Benjamin Arras, Christian Houdré
We explore connections between covariance representations, Bismut-type formulas and Stein's method. First, using the theory of closed symmetric forms, we derive covariance represen…
A stroll along the gamma
Benjamin Arras, Yvik Swan
We provide the first in-depth study of the "smart path" interpolation between an arbitrary probability measure and the gamma- distribution. We propose new explicit repres…
On Stein's Method for Multivariate Self-Decomposable Laws
Benjamin Arras, Christian Houdré
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…
Sequential sampling for optimal weighted least squares approximations in hierarchical spaces
Benjamin Arras, Markus Bachmayr, Albert Cohen
We consider the problem of approximating an unknown function from its evaluations at given sampling points , where is a…
A bound on the 2-Wasserstein distance between linear combinations of independent random variables
Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly +1
We provide a bound on a natural distance between finitely and infinitely supported elements of the unit sphere of , the space of real valued sequences with fi…
A new approach to the Stein-Tikhomirov method: with applications to the second Wiener chaos and Dickman convergence
Benjamin Arras, Guillaume Mijoule, Guillaume Poly +1
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, r…
On Stein's Method for Infinitely Divisible Laws With Finite First Moment
Benjamin Arras, Christian Houdré
We present, in a unified way, a Stein methodology for infinitely divisible laws (without Gaussian component) having finite first moment. Based on a correlation representation, we o…
Stein's method on the second Wiener chaos : 2-Wasserstein distance
Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly +1
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…
Stein characterizations for linear combinations of gamma random variables
Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly +1
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…
On a class of self-similar processes with stationary increments in higher order Wiener chaoses
Benjamin Arras
We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wave…