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Asymptotic expansions for potential functions of i.i.d. random fields
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  • Published: August 1989

Asymptotic expansions for potential functions of i.i.d. random fields

  • F. Götze1 &
  • C. Hipp2 

Probability Theory and Related Fields volume 82, pages 349–370 (1989)Cite this article

Summary

For sums of finite range potential functions of an iid random field we derive the validity of formal expansions of length two. Under standard conditions, formal expansions are valid if and only if the characteristic functions of the sum converge to zero for all nonzero frequency parameters. If this convergence fails, the distribution of the sum can be approximated by a mixture of lattice distributions. The result applies to m-dependent random fields generated by independent random variables.

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Bielefeld, Universitätsstraße, D-4800, Bielefeld, Germany

    F. Götze

  2. FB Mathematik, Universität Hamburg, Bundesstr. 55, D-2000, Hamburg, Germany

    C. Hipp

Authors
  1. F. Götze
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  2. C. Hipp
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Götze, F., Hipp, C. Asymptotic expansions for potential functions of i.i.d. random fields. Probab. Th. Rel. Fields 82, 349–370 (1989). https://doi.org/10.1007/BF00339992

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  • Received: 14 November 1986

  • Revised: 24 February 1989

  • Issue Date: August 1989

  • DOI: https://doi.org/10.1007/BF00339992

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Keywords

  • Stochastic Process
  • Standard Condition
  • Characteristic Function
  • Probability Theory
  • Asymptotic Expansion
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