Generalized weak laws of large numbers in Hilbert spaces

Mengmeng Chang and Yu Miao

Statistics & Probability Letters, 2023, vol. 197, issue C

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.

Keywords: Weak law of large numbers; Coordinatewise widely orthant dependent random vectors; Pairwise and coordinatewise negative dependent random vectors; Hilbert space (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spl.2023.109830

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