We analyze the p-random Wishart tensor (p≥ 2) associated with an initial n× d random
matrix X n, d whose entries are independent and belong to the Wiener chaos. The order of …

We consider a modified quadratic variation of the Hermite process based on some well-
chosen increments of this process. These special increments have the very useful property …

This thesis explores convergence phenomena and statistical methodologies within high-
dimensional frameworks. The first aspect investigates the convergence behavior of the …

We consider an× d random matrix X n, d whose entries are the spatial increments of the
solution to the stochastic heat equation with space-time white noise. We analyze the limit …

In this paper, we characterize the convergence of the (rescaled logarithmic) empirical
spectral distribution of wavelet random matrices. We assume a moderately high-dimensional …

We study the high-dimensional asymptotic regimes of correlated Wishart matrices d− 1 𝒴 𝒴
T, where 𝒴 is an× d Gaussian random matrix with correlated and non-stationary entries. We …

In this note, we study the Gaussian fluctuations for the Wishart matrices d− 1 X n, d X n, d T,
where X n, d is an× d random matrix whose entries are jointly Gaussian and correlated with …

We consider anxd random matrix Xn, d whoses entries can be expressed as Skorohod
integrals. By using the techniques of the Malliavin calculus, we study the fluctuations under …

We define an asymptotically normal wavelet-based strongly consistent estimator for the
Hurst parameter of any Hermite processes. This estimator is obtained by considering a …

In this paper, we construct the wavelet eigenvalue regression methodology (Abry and Didier
in J Multivar Anal 168: 75–104, 2018a; in Bernoulli 24 (2): 895–928, 2018b) in high …