We study the distribution of a fully connected neural network with random Gaussian weights
and biases in which the hidden layer widths are proportional to a large constant $ n $. Under …

We derive upper bounds on the Wasserstein distance (W 1), with respect to sup-norm,
between any continuous R d valued random field indexed by the n-sphere and the …

In this paper, we study the spatial averages of the solution to the parabolic Anderson model
driven by a space-time Gaussian homogeneous noise that is colored in both time and …

In this article, we study the hyperbolic Anderson model driven by a space-time colored
Gaussian homogeneous noise with spatial dimension d= 1, 2. Under mild assumptions, we …

We establish new explicit bounds on the Gaussian approximation of Poisson functionals
based on novel estimates of moments of Skorohod integrals. Combining these with the …

There is a recent and growing literature on large-width asymptotic and non-asymptotic
properties of deep Gaussian neural networks (NNs), namely NNs with weights initialized as …

In this paper, we study one-dimensional hyperbolic Anderson models (HAM) driven by
space-time pure-jump Lévy white noise in a finite-variance setting. Motivated by recent …

This paper studies the minimum mean squared error (MMSE) of estimating X∈ ℝ d from the
noisy observation Y∈ ℝ k, under the assumption that the noise (ie, Y| X) is a member of the …

In this PhD thesis, we apply a combination of Malliavin calculus and Stein's method in the
framework of probability approximations. The specific problems we tackle with these …

Initiated around the year 2007, the Malliavin–Stein approach to probabilistic approximations
combines Stein's method with infinite-dimensional integration by parts formulae based on …