Let $X_i$ be a stationary moving average with long-range dependence. Suppose $EX_i = 0$ and $EX^{2n}_i < \infty$ for some $n \geq 2$. When the $X_i$ are Gaussian, then the Hermite polynomials play a fundamental role in the study of noncentral limit theorems for functions of $X_i$. When the $X_i$ are not Gaussian, the relevant polynomials are Appell polynomials. They satisfy a multinomial-type expansion that can be used to establish noncentral limit theorems.
@article{1176992170,
author = {Avram, Florin and Taqqu, Murad S.},
title = {Noncentral Limit Theorems and Appell Polynomials},
journal = {Ann. Probab.},
volume = {15},
number = {4},
year = {1987},
pages = { 767-775},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992170}
}
Avram, Florin; Taqqu, Murad S. Noncentral Limit Theorems and Appell Polynomials. Ann. Probab., Tome 15 (1987) no. 4, pp. 767-775. http://gdmltest.u-ga.fr/item/1176992170/