The variance-gamma (VG) distributions form a four-parameter family which includes as
special and limiting cases the normal, gamma and Laplace distributions. Some of the …

The product of two zero mean correlated normal random variables, and more generally the
sum of independent copies of such random variables, has received much attention in the …

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 establish general upper bounds on the Kolmogorov distance between two probability
distributions in terms of the distance between these distributions as measured with respect …

Inspired by the insightful article [4], we revisit the Nualart–Peccati criterion [13](now known
as the Fourth Moment Theorem) from the point of view of spectral theory of general Markov …

We study rates of convergence in central limit theorems for partial sums of polynomial
functionals of general stationary and asymptotically stationary Gaussian sequences, using …

We extend Stein's celebrated Wasserstein bound for normal approximation via
exchangeable pairs to the multi-dimensional setting. As an intermediate step, we exploit the …

We develop techniques for determining an explicit Berry–Esseen bound in the Kolmogorov
distance for the normal approximation of a ratio of Gaussian functionals. We provide an …

We combine Malliavin calculus with Stein's method to derive bounds for the Variance-
Gamma approximation of functionals of isonormal Gaussian processes, in particular of …

We provide a bound on a distance between finitely supported elements and general
elements of the unit sphere of ℓ 2 (N∗). We use this bound to estimate the Wasserstein-2 …