Workshop MESA - Stein's Method and Applications

Contribution List

10. Central convergence on Wiener chaoses always implies asymptotic smoothness and C-infinite convergence of densities

Guillaume Poly (IRMAR, Université de Rennes 1)

3/21/23, 9:45 AM

Let (F n) be any sequence of Wiener chaoses of any fixed
order converging in distribution towards a standard Gaussian. In this talk, without any
additional assumptions, we shall explain how to derive the asymptotic smoothness of
the densities of F n , as well...

6. Régularité des lois de formes quadratiques en des variables iid : une approche par forme de Dirichlet

Ronan Herry (IRMAR, Université de Rennes 1)

3/21/23, 11:15 AM

Nous présentons une nouvelle approche pour étudier la régularité de la loi d'une variable aléatoire quand l'espace de probabilité est équipé d'une forme de Dirichlet. Plus précisément nous développons une nouvelle technique pour contrôler les moments négatifs du carré du champ d'une variable aléatoire et utilisons le résultat (bien connu) qu'un tel contrôle implique un contrôle sur les normes...

3. Exponential convergence of Sinkhorn algorithm for quadratic entropic optimal transport

Giovanni Conforti (CMAP École Polytechnique)

3/21/23, 2:00 PM

Over the past decade, Entropic Optimal Transport problem has emerged as a versatile and computationally more tractable proxy for the Optimal Transport (Monge-Kantorovich) problem for applications in data science and statistical machine learning. One of the reasons behind the interest in adding an entropic penalty in the Monge Kantorovich problem is the fact that solutions can be computed by...

11. Stein's method for stability estimates of the Poincaré constant

Jordan Serres (CREST - ENSAE)

3/21/23, 2:55 PM

The Poincaré inequality governs the exponential convergence rate of algorithms such as Langevin dynamics. Interesting questions are then to understand how the Poincaré constant changes when the dynamics is perturbed, or to understand when this constant is minimal under certain constraints. In this talk, I will present some such results in the context of Markov diffusions. Their proof is based...

5. Malliavin calculus for marked binomial processes and Chen-Stein method

Hélène Halconruy (ESILV)

3/21/23, 4:20 PM

We can observe a clumping phenomenon when counting the number of series of $t$ heads in a sequence of independent coin tosses or the occurrences of a rare word in a DNA sequence. The Chen-Stein method is an efficient tool to limit the approximation error when the law of the number of clusters can be approximated by a Poisson law (possibly compound).
We revisit this method by reducing these...

9. The normal approximation of compound Hawkes functionals

Mahmoud Khabou (IMT, Université de Toulouse)

3/22/23, 9:00 AM

Joint work with N. Privault and A. Réveillac

We derive quantitative bounds in the Wasserstein distance for the approximation of stochastic integrals of deterministic and non-negative integrands with respect to Hawkes processes by a normally distributed random variable. Our results are specifically applied to compound Hawkes processes, and improve on the current literature where estimates...

8. Total variation bound for Hadwiger's functional using Stein's method

Ivan Nourdin (University of Luxembourg)

3/22/23, 10:25 AM

Let $K$ be a convex body in $\mathbb{R}^d$. Let $X_K$ be a $d$-dimensional random vector distributed according to the Hadwiger-Wills density $\mu_K$ associated with $K$, defined as $\mu_K(x)=ce^{-\pi {\rm dist}^2(x,K)}$, $x\in \mathbb{R}^d$. Finally, let the information content $H_K$ be defined as $H_K={\rm dist}^2(X_K,K)$.

In this talk, we will study the fluctuations of $H_K$ around its...

4. Invertibility of functionals of the Poisson process and applications

Laurent Decreusefond (LTCI, Télécom Paris)

3/22/23, 11:20 AM

Joint work with L. Coutin

Solving the SDE $dX(t)=r(X(t)) dt + dB(t) (1)$ is equivalent invert the map $B\mapsto B(t)-\int_0^t r(B(s)) ds$.
We study the analog of this problem on the Poisson space. Because of the Girsanov Theorem, it turns out that equivalent problem consists in inverting a time change.
We can then reinterpret the solution of the generalized Hawkes problem (find a self...

7. Second order Poincaré inequalities and applications to geometric functionals

Raphaël Lachièze-Rey (MAP5, Université de Paris)

3/23/23, 9:45 AM

Stein's method applied to orthogonal decompositions has allowed to establish second order Poincaré inequalities for random functionals of binomial input and Poisson input. We will show how to apply these inequalities, and in particular how they enabled to show limit theorems for geometric functionals for random processes defined on the Euclidean space or a smooth manifold.

1. Quantitative Generalized CLT with Self-Decomposable Limiting Laws by Spectral Methods

Benjamin Arras (Laboratoire Paul Painlevé, Université de Lille)

3/23/23, 11:10 AM

In this talk, I will present new stability results for non-degenerate centered self-decomposable laws with finite second moment and for non-degenerate symmetric alpha-stable laws with alpha in (1,2). These stability results are based on Stein's method and closed forms techniques.
As an application, explicit rates of convergence are obtained for several instances of the generalized CLTs.

2. Intertwinings and Stein's magic factors for birth-death processes

Bertrand Cloez (INRAE Montepellier)

3/23/23, 2:00 PM

We present some quantitative bounds on the so-called Stein magic factors of discrete distributions. These ones are obtained from intertwining relations between Markov semigroups of birth-death processes and discrete gradients. We also illustrate the application of this Stein magic factors for the convergence of the binomial negative law to the Poisson one.

12. Central Limit Theorems for Poisson Random Waves

Anna Paola Todino (Università degli Studi di Milano-Bicocca)

3/23/23, 2:55 PM

We introduce a model of Poisson random waves in S^2 and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the frequency of the waves (eigenfunctions) diverge to infinity. We consider finite-dimensional distributions, harmonic coefficients and convergence in law in functional spaces, and we investigate carefully the interplay between the rate of...