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Volume 57, Issue 4
B-Statistical Uniform Integrability and $\mathfrak{L}_p$ Convergence

Mengru Chen, Weicai Peng & Zhongzhi Wang

DOI: 10.4208/jms.v57n4.24.03

J. Math. Study, 57 (2024), pp. 446-459.

Published online: 2024-12

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  • 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.

  • Keywords

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

  • AMS Subject Headings

60F25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JMS-57-446, author = {Chen , MengruPeng , Weicai and Wang , Zhongzhi}, title = {B-Statistical Uniform Integrability and $\mathfrak{L}_p$ Convergence}, journal = {Journal of Mathematical Study}, year = {2024}, volume = {57}, number = {4}, pages = {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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v57n4.24.03}, url = {http://global-sci.org/intro/article_detail/jms/23711.html} }
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 -

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.

Chen , MengruPeng , Weicai and Wang , Zhongzhi. (2024). B-Statistical Uniform Integrability and $\mathfrak{L}_p$ Convergence. Journal of Mathematical Study. 57 (4). 446-459. doi:10.4208/jms.v57n4.24.03
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