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Generalized weak laws of large numbers in Hilbert spaces

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  • Chang, Mengmeng
  • Miao, Yu

Abstract

In this paper, the weak laws of large numbers for weighted sums and random sums of H-valued dependent random vectors are established, which include and generalize some known results. As an application, the concept of CWOD random vectors is introduced and the corresponding weak laws of large numbers for weighted sums and random sums cases are obtained. Furthermore, to complete the work of Anh and Hien (2021), the weak law of large numbers for random sums of PCND random vectors is also presented.

Suggested Citation

  • Chang, Mengmeng & Miao, Yu, 2023. "Generalized weak laws of large numbers in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:stapro:v:197:y:2023:i:c:s0167715223000548
    DOI: 10.1016/j.spl.2023.109830
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    References listed on IDEAS

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    1. Mi-Hwa Ko & Tae-Sung Kim & Kwang-Hee Han, 2009. "A Note on the Almost Sure Convergence for Dependent Random Variables in a Hilbert Space," Journal of Theoretical Probability, Springer, vol. 22(2), pages 506-513, June.
    2. Kunpeng Wang & Xuejun Wang, 2020. "Strong convergence properties for partial sums of asymptotically negatively associated random vectors in Hilbert spaces," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(22), pages 5578-5586, November.
    3. Mi-Hwa Ko, 2018. "Complete convergence for coordinatewise asymptotically negatively associated random vectors in Hilbert spaces," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(3), pages 671-680, February.
    4. Hien, N.T.T. & Thanh, L.V., 2015. "On the weak laws of large numbers for sums of negatively associated random vectors in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 236-245.
    5. Son Cong Ta & Cuong Manh Tran & Dung Van Le, 2020. "On the almost sure convergence for sums of negatively superadditive dependent random vectors in Hilbert spaces and its application," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(11), pages 2770-2786, June.
    6. Yang Ding & Yi Wu & Songlin Ma & Xinran Tao & Xuejun Wang, 2017. "Complete convergence and complete moment convergence for widely orthant-dependent random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 8278-8294, August.
    7. Rosalsky, Andrew & Thành, Lê Vǎn, 2021. "A note on the stochastic domination condition and uniform integrability with applications to the strong law of large numbers," Statistics & Probability Letters, Elsevier, vol. 178(C).
    8. Ko, Mi-Hwa, 2018. "On complete moment convergence for CAANA random vectors in Hilbert spaces," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 104-110.
    9. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
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