Empirical limit theorems for Wiener chaos

Published 24 Oct 2023 in math.PR, math.ST, and stat.TH | (2310.15462v4)

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-It^o integrals are established.

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