Zobrazeno 1 - 10
of 97
pro vyhledávání: '"Bourguin, Solesne"'
We establish the convergence of the densities of a sequence of nonlinear functionals of an underlying Gaussian process to the density of a Gamma distribution. The key idea of our work is a new density formula for random variables in the setting of Ma
Externí odkaz:
http://arxiv.org/abs/2406.12722
We study fluctuations of small noise multiscale diffusions around their homogenized deterministic limit. We derive quantitative rates of convergence of the fluctuation processes to their Gaussian limits in the appropriate Wasserstein metric requiring
Externí odkaz:
http://arxiv.org/abs/2301.09005
Publikováno v:
journal of Theoretical Probability, 36, Article number: 1 (2023)
In this paper we study the moderate deviations principle (MDP) for slow-fast stochastic dynamical systems where the slow motion is governed by small fractional Brownian motion (fBm) with Hurst parameter $H\in(1/2,1)$. We derive conditions on the mode
Externí odkaz:
http://arxiv.org/abs/2206.06794
We introduce a model of Poisson random waves in $\mathbb{S}^{2}$ and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., frequency) of the waves (eigenfunctions) diverge to infinity. We conside
Externí odkaz:
http://arxiv.org/abs/2203.04721
We develop a functional Stein-Malliavin method in a non-diffusive Poissonian setting, thus obtaining a) quantitative central limit theorems for approximation of arbitrary non-degenerate Gaussian random elements taking values in a separable Hilbert sp
Externí odkaz:
http://arxiv.org/abs/2110.04877
Autor:
Bourguin, Solesne, Dang, Thanh
Publikováno v:
Random Matrices: Theory and Applications, Vol. 11, No. 01, 2250006 (2022)
We study the high-dimensional asymptotic regimes of correlated Wishart matrices $d^{-1}\mathcal{Y}\mathcal{Y}^T$, where $\mathcal{Y}$ is a $n\times d$ Gaussian random matrix with correlated and non-stationary entries. We prove that under different no
Externí odkaz:
http://arxiv.org/abs/2011.01199
We study the fluctuations, as $d,n\to \infty$, of the Wishart matrix $\mathcal{W}_{n,d}= \frac{1}{d} \mathcal{X}_{n,d} \mathcal{X}_{n,d}^{T} $ associated to a $n\times d$ random matrix $\mathcal{X}_{n,d}$ with non-Gaussian entries. We analyze the lim
Externí odkaz:
http://arxiv.org/abs/2008.02120
We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimators for both the Hurst index as well as a vector of unknown parameters
Externí odkaz:
http://arxiv.org/abs/2007.11665
This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we character
Externí odkaz:
http://arxiv.org/abs/1906.02131
Autor:
Bourguin, Solesne, Campese, Simon
We introduce a framework to derive quantitative central limit theorems in the context of non-linear approximation of Gaussian random variables taking values in a separable Hilbert space. In particular, our method provides an alternative to the usual
Externí odkaz:
http://arxiv.org/abs/1905.05127