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