Convolutions of Bivariate Appell Polynomials with Long-Range Dependence

Norma Terrin


The convergence in distribution of a quadratic form of a non-instantaneous, non-linear bivariate filter is established. The input to the filter is assumed to have long memory, but is not necessarily Gaussian. The limit is representable as a multiple Wiener-Itô integral. While instantaneous functions of long-memory processes typically have limit theorems with normalization exponents greater than or equal to 1/2, for the non-instantaneous filter studied here, exponents less than 1/2 are possible.

Keywords and Phrases: long memory, multiple Wiener-Itô integrals, quadratic forms, non-instantaneous, non-linear, power counting.