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Non-central Limit Theorems

  • Péter Major
Chapter
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.

References

  1. 3.
    Breuer, P., Major, P.: Central limit theorems for non-linear functionals of Gaussian fields. J. Multivar. Anal. 13(3), 425–441 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 9.
    Dobrushin, R.L., Major, P.: Non-central limit theorems for non-linear functionals of Gaussian fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 50, 27–52 (1979)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 13.
    Dudley, R.M.: Distances of probability measures and random variables. Ann. Math. Stat. 39, 1563–1572 (1968)zbMATHMathSciNetGoogle Scholar
  4. 25.
    Major, P.: Limit theorems for non-linear functionals of Gaussian sequences. Z. Wahrscheinlichkeitstheorie verw. Gebiete 57, 129–158 (1981)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Péter Major
    • 1
  1. 1.Alfréd Rényi Mathematical Institute Hungarian Academy of SciencesBudapestHungary

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