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B-Statistical Uniform Integrability and $\mathfrak{L}_p$ Convergence

B-Statistical Uniform Integrability and $\mathfrak{L}_p$ Convergence

Year:    2024

Author:    Mengru Chen, Weicai Peng, Zhongzhi Wang

Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 446–459

Abstract

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v57n4.24.03

Journal of Mathematical Study, Vol. 57 (2024), Iss. 4 : pp. 446–459

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    B-statistical uniform integral Cesàro matrix martingale difference $\mathfrak{L}_p$ convergence.

Author Details

Mengru Chen

Weicai Peng

Zhongzhi Wang