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Non-central Limit Theorems

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Part of the Lecture Notes in Mathematics book series (LNM,volume 849)

Abstract

Here we present some non-trivial limit theorems where the limit is a non-Gaussian self-similar field. The results of the previous chapters may explain at a heuristic level why such results should hold. But a rigorous proof demands much extra work whose consequences may be interesting in themselves.

Keywords

  • Heuristic Level
  • Prokhorov Metric
  • Regular Diagram
  • Vague Convergence
  • Stationary Gaussian Random Field

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References

  1. Breuer, P., Major, P.: Central limit theorems for non-linear functionals of Gaussian fields. J. Multivar. Anal. 13(3), 425–441 (1983)

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  4. Major, P.: Limit theorems for non-linear functionals of Gaussian sequences. Z. Wahrscheinlichkeitstheorie verw. Gebiete 57, 129–158 (1981)

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Major, P. (2014). Non-central Limit Theorems. In: Multiple Wiener-Itô Integrals. Lecture Notes in Mathematics, vol 849. Springer, Cham. https://doi.org/10.1007/978-3-319-02642-8_8

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