Lacunary Series and Stable Distributions View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2015

AUTHORS

István Berkes , Robert Tichy

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 \((X_n)\) of random variables to have a subsequence \((X_{n_k})\) whose weighted partial sums, suitably normalized, converge weakly to a symmetric stable distribution with parameter \(0<\alpha <2\). More... »

PAGES

7-19

References to SciGraph publications

  • 1989-09. Almost sure and weak invariance principles for random variables attracted by a stable law in PROBABILITY THEORY AND RELATED FIELDS
  • 1970-09. A general strong law in INVENTIONES MATHEMATICAE
  • 1965-09. On a problem of Steinhaus in ACTA MATHEMATICA
  • 1977-03. Limit theorems for subsequences of arbitrarily-dependent sequences of random variables in PROBABILITY THEORY AND RELATED FIELDS
  • 1989-09. On almost symmetric sequences inLp in ACTA MATHEMATICA HUNGARICA
  • 1986-09. Exchangeable random variables and the subsequence principle in PROBABILITY THEORY AND RELATED FIELDS
  • 1974-09. A subsequence principle in probability theory in INVENTIONES MATHEMATICAE
  • 1974-12. Every sequence converging toO weakly inL2 contains an unconditional convergence sequence in ARKIV FÖR MATEMATIK
  • 1985-12. Almost exchangeable sequences of random variables in PROBABILITY THEORY AND RELATED FIELDS
  • 1972. Un principe de sous-suites dans la théorie des probabilités in SÉMINAIRE DE PROBABILITÉS VI UNIVERSITÉ DE STRASBOURG
  • 1967-03. A generalization of a problem of Steinhaus in ACTA MATHEMATICA
  • Book

    TITLE

    Mathematical Statistics and Limit Theorems

    ISBN

    978-3-319-12441-4
    978-3-319-12442-1

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-12442-1_2

    DOI

    http://dx.doi.org/10.1007/978-3-319-12442-1_2

    DIMENSIONS

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    148 schema:name Institute of Mathematics A, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria
    149 Institute of Statistics, Graz University of Technology, Kopernikusgasse 24, Graz, Austria
    150 rdf:type schema:Organization
     




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