Stein's method for nonconventional sums

Yeor Hafouta

We obtain almost optimal convergence rate in the central limit theorem for "nonconevntional" sums of the form $S_N=N^{-\frac{1}{2}}{\sum }_{n=1}^N(F({\xi }_n,{\xi }_{2n},...,{\xi }_{\ell n})-\bar{F})$.