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A complete convergence theorem for row sums from arrays of rowwise independent random elements in Rademacher type p Banach spaces. II
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A complete convergence theorem for row sums from arrays of rowwise independent random elements in Rademacher type p Banach spaces. II

Tien-Chung Hu, Andrew Rosalsky, Andrei Volodin 和 Sen Zhang
Stochastic Analysis and Applications, 頁碼.1-17
2020
DOI: https://doi.org/10.1080/07362994.2020.1791721

摘要

60B12 array of Banach space valued random elements Complete convergence Primary 60F15 Rademacher type p Banach space rowwise independent Secondary 60B11 Statistics and Probability Statistics Probability and Uncertainty Applied Mathematics
In this correspondence, for an array of rowwise independent random elements (Formula presented.) taking values in a real separable Rademacher type (Formula presented.) Banach space and a sequence of positive constants (Formula presented.) the main result provides conditions for the complete convergence result (Formula presented.) to hold. The complete convergence does not necessary hold if the Rademacher type p hypothesis is dispensed with. Corollaries of the main result are obtained and illustrative examples are presented.

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