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Almost Sure Convergence of the General Jamison Weighted Sum of \( {\user1{B}} \)-Valued Random Variables

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Abstract

In this paper, two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods, their properties and relationships are systematically discussed. We also analysed the implication of the conditions in previous papers. Then we apply these consequences to \( {\user1{B}} \)-valued random variables, and greatly improve the original results of the strong convergence of the general Jamison weighted sum. Furthermore, our discussions are useful to the corresponding questions of real-valued random variables.

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Authors and Affiliations

  1. Department of Statistics and Finance, University of Science and Technology of China, Hefei, 230026, P. R. China

    Chun Su & Tie Jun Tong

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  1. Chun Su
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  2. Tie Jun Tong
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Correspondence to Chun Su.

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Research supported by National Science Foundation of China (No.10071081) and special financial support of Chinese Academy of Sciences

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Su, C., Tong, T.J. Almost Sure Convergence of the General Jamison Weighted Sum of \( {\user1{B}} \)-Valued Random Variables. Acta Math Sinica 20, 181–192 (2004). https://doi.org/10.1007/s10114-003-0286-y

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  • DOI: https://doi.org/10.1007/s10114-003-0286-y

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