Nonconventional Polynomial CLT

Abstract

We obtain a functional central limit theorem (CLT) for sums of the form ${\xi }_N(t)=\frac{1}{\sqrt{N}}{\sum }_{n=1}^{[Nt]}(F(X(q_1(n)),...,X(q_{\ell }(n)))-\bar{F})$ where $q_1,...,q_{\ell }$ are polynomials.

arXiv comment38 pages