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Multivariate Appell polynomials and the central limit theorem

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Dependence in Probability and Statistics

Part of the book series: Progress in Probability and Statistics ((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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Authors
  1. L. Giraitis
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  2. D. Surgailis
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Editor information

Editors and Affiliations

  1. Institut für Mathematische Stochastik, Universität Freiburg, 7800, Freiburg i. Br., Federal Republic of Germany

    Ernst Eberlein

  2. Department of Mathematics, Boston University, 02215, Boston, MA, USA

    Murad S. Taqqu

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© 1986 Springer Science+Business Media New York

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Giraitis, L., Surgailis, D. (1986). Multivariate Appell polynomials and the central limit theorem. In: Eberlein, E., Taqqu, M.S. (eds) Dependence in Probability and Statistics. Progress in Probability and Statistics, vol 11. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4615-8162-8_2

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  • DOI: https://doi.org/10.1007/978-1-4615-8162-8_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4615-8163-5

  • Online ISBN: 978-1-4615-8162-8

  • eBook Packages: Springer Book Archive

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