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**Convolutions of Bivariate Appell
Polynomials with Long-Range Dependence**

**Norma Terrin**

### Abstract:

*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.