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Lacunary Series and Stable Distributions

In: Mathematical Statistics and Limit Theorems

Author

Listed:
  • István Berkes

    (Graz University of Technology, Institute of Statistics)

  • Robert Tichy

    (Graz University of Technology, Institute of Mathematics A)

Abstract

By well-known results of probability theory, any sequence of random variables with bounded second moments has a subsequence satisfying the central limit theorem and the law of the iterated logarithm in a randomized form. In this paper we give criteria for a sequence $$(X_n)$$ ( X n ) of random variables to have a subsequence $$(X_{n_k})$$ ( X n k ) whose weighted partial sums, suitably normalized, converge weakly to a symmetric stable distribution with parameter $$0

Suggested Citation

  • István Berkes & Robert Tichy, 2015. "Lacunary Series and Stable Distributions," Springer Books, in: Marc Hallin & David M. Mason & Dietmar Pfeifer & Josef G. Steinebach (ed.), Mathematical Statistics and Limit Theorems, edition 127, pages 7-19, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12442-1_2
    DOI: 10.1007/978-3-319-12442-1_2
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