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Non-central limit theorems and Appell polynomials
Murad S. Taqqu
Let be a stationary moving average with long-range dependence.
Suppose and for some .
When the are Gaussian, then
the Hermite polynomials play a fundamental role in the study of
non-central limit theorems for functions of .
When the are not Gaussian, the relevant
polynomials are Appell polynomials. They satisfy a multinomial type
expansion that can be used to establish non-central limit theorems.