The Annals of Probability

Noncentral Limit Theorems and Appell Polynomials

Florin Avram and Murad S. Taqqu

Full-text: Open access

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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 33A70

Keywords
Appell polynomials self-similar processes multiple Wiener-Ito integrals long-range dependence weak convergence Hermite processes

Citation

Avram, Florin; Taqqu, Murad S. Noncentral Limit Theorems and Appell Polynomials. Ann. Probab. 15 (1987), no. 2, 767--775. doi:10.1214/aop/1176992170. https://projecteuclid.org/euclid.aop/1176992170


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