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Multivariate Appell polynomials and the central limit theorem

  • L. Giraitis
  • D. Surgailis
Part of the Progress in Probability and Statistics book series (PRPR, volume 11)

Summary

A CLT for processes of the form L(Xt) is proved, where L(x) is a polynomial and Xt, t ∈ ℤ is a process with long range dependence. Conditions on Xt are formulated in terms of semi-invariants; they are specified for linear processes Xt. The notion of the Appell rank of L(x) plays a basic role in the CLT. Various topics related to Appell polynomials (e.g. expansions, diagram formalism for semi-invariants) are discussed.

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© Springer Science+Business Media New York 1986

Authors and Affiliations

  • L. Giraitis
  • D. Surgailis

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