Hauptmenü
  • Autor
    • Berkes, István
    • Tichy, Robert
  • TitelLacunary series and stable distributions
  • Volltext
  • DOI10.1007/978-3-319-12442-1_2
  • Erschienen inMathematical Statistics and Limit Theorems
  • Erscheinungsjahr2015
  • Seiten7-19
  • LicenceCC BY
  • ISBN978-3-319-12442-1
  • ZugriffsrechteCC-BY
  • Download Statistik38
  • Peer ReviewJa
  • AbstractBy 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 \(0<\alpha <2\).