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Nonconventional Polynomial CLT (1504.00655v5)
Published 2 Apr 2015 in math.PR
Abstract: We obtain a functional central limit theorem (CLT) for sums of the form $\xi_N(t)=\frac1{\sqrt N}\sum_{n=1}{[Nt]}\big(F(X(q_1(n)),...,X(q_\ell(n)))-\bar F\big)$ where $q_1,...,q_\ell$ are polynomials.