A functional CLT for nonconventional polynomial arrays
A functional CLT for nonconventional polynomial arrays
<p style='text-indent:20px;'>In this paper we will prove a functional central limit theorem (CLT) for random functions of the form <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ {\mathcal S}_N(t) = N^{-\frac12}\sum\limits_{n = 1}^{[Nt]} F(\xi_{q_1(n, N)}, \xi_{q_2(n, N)}, ..., \xi_{q_\ell(n, N)}) $\end{document} </tex-math></disp-formula> <p style='text-indent:20px;'>where the <inline-formula><tex-math id="M1">\begin{document}$ q_i $\end{document}</tex-math></inline-formula>'s are certain type …