# Two-dimensional Gram-Charlier reconstruction of velocity correlations

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Presents a study on the use of Hermite polynomials in the estimation of risk-neutral and statistical densities. Application of model to price options on Eurodollar futures; Derivation and testing of the restrictions; Comparison between out-of-sample four-parameter model and two-parameter version.

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Properties of the extended Hermite polynomials are studied. It is proved, apparently for the first time, that these functions (times Gaussian functions) are the modes of an n-dimensional first-order system, thus generalizing an earlier result due to Hardy, Sheng, and Siegman for one dimension....

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The products of several orthogonal polynomials of boson field operators, the quantum mechanical version of multiple Wiener integrals, are expressed as linear combinations of the polynomials. The expression is obtained by making use of the correspondence rules of boson operators and complex numbers.