Journal articles
Year
2020
Abstract
We combine the method of exchangeable pairs with Stein’s method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply this approach to estimate the distance of a sum of random variables, chosen from an array according to a random permutation, from a Gaussian mixture process. This result lets us prove a functional combinatorial central limit theorem. We also consider a graph-valued process and bound the speed of convergence of the distribution of its rescaled edge counts to a continuous Gaussian process.
KASPRZAK, M. (2020). Functional approximations via Stein’s method of exchangeable pairs. Annales de l Institut Henri Poincare-Probabilites et Statistiques, 56(4).