## The Annals of Probability

### Noncentral Limit Theorems and Appell Polynomials

#### Abstract

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 information

Source
Ann. Probab., Volume 15, Number 2 (1987), 767-775.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992170

Digital Object Identifier
doi:10.1214/aop/1176992170

Mathematical Reviews number (MathSciNet)
MR885142

Zentralblatt MATH identifier
0624.60049

JSTOR