On the concept of B-statistical uniform integrability of weighted sums of random variables and the law of large numbers with mean convergence in the statistical sense

Cabrera M. O., Rosalsky A., ÜNVER M., Volodin A.

TEST, cilt.30, sa.1, ss.83-102, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 1
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s11749-020-00706-2
  • Dergi Adı: TEST
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, EconLit, zbMATH, DIALNET
  • Sayfa Sayıları: ss.83-102
  • Anahtar Kelimeler: Sequence of random variables, Uniform integrability, Statistical convergence, POSITIVE LINEAR-OPERATORS, THEOREMS, SUMMABILITY, SPACES, APPROXIMATION
  • Ankara Üniversitesi Adresli: Evet

Özet

In this correspondence, for a nonnegative regular summability matrix B and an array {ank} of real numbers, the concept of B-statistical uniform integrability of a sequence of random variables {Xk} with respect to {ank} is introduced. This concept is more general and weaker than the concept of {Xk} being uniformly integrable with respect to {ank}. Two characterizations of B-statistical uniform integrability with respect to {ank} are established, one of which is a de La Vallee Poussin-type characterization. For a sequence of pairwise independent random variables {Xk} which is B-statistically uniformly integrable with respect to {ank}, a law of large numbers with mean convergence in the statistical sense is presented for 8 k=1 ank( Xk - EXk) as n. 8. A version is obtained without the pairwise independence assumption by strengthening other conditions.