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 …

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 …

A quantitative central limit theorem for the simple symmetric exclusion process (SSEP) on a
$ d $-dimensional discrete torus is proven. The argument is based on a comparison of the …

We develop a general approach to Stein's method for approximating a random process in
the path space D ([0, T]→ R d) by a real continuous Gaussian process. We then use the …

Let S n be a sum of independent identically distribution random variables with finite first
moment and h M be a call function defined by g M (x)= max {x− M, 0} for x∈ R, M> 0. In this …

Stochastic iterative algorithms, including stochastic gradient descent (SGD) and stochastic
gradient Langevin dynamics (SGLD), are widely utilized for optimization and sampling in …

The distribution of the maximum of a zero truncated Poisson number of iid exponentially
distributed random variables is known as a Poisson-Exponential distribution. It arises for …

Abstract In 1972, Charles Stein introduced a novel approach to deriving distributional
approx-imations in probability theory, allowing one to obtain explicit bounds with respect to a …