TY - JOUR
T1 - B-Statistical Uniform Integrability and $\mathfrak{L}_p$ Convergence
AU - Chen , Mengru
AU - Peng , Weicai
AU - Wang , Zhongzhi
JO - Journal of Mathematical Study
VL - 4
SP - 446
EP - 459
PY - 2024
DA - 2024/12
SN - 57
DO - http://doi.org/10.4208/jms.v57n4.24.03
UR - https://global-sci.org/intro/article_detail/jms/23711.html
KW - B-statistical uniform integral, Cesàro matrix, martingale difference, $\mathfrak{L}_p$ convergence.
AB - <p style="text-align: justify;">In this paper, we first give the concept of B-statistical uniform integrability
with respect to Cesàro matrix (B-CUI), which is weaker than Cesàro uniform integrability. Then we establish some B-statistical convergence theorems for random sequence
under the condition of B-CUI, which generalizes the outcomes of some known results.
Finally, for some special kinds of triangular array or pairwise independent sequences
of random variables, similar results are also derived without conditions of B-CUI.</p>