Empirical limit theorems for Wiener chaos
arXiv:2310.15462 · doi:10.1016/j.spl.2024.110222
Abstract
We consider empirical measures in a triangular array setup with underlying distributions varying as sample size grows. We study asymptotic properties of multiple integrals with respect to normalized empirical measures. Limit theorems involving series of multiple Wiener-Itô integrals are established.