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<p>In this paper, we propose a novel normalization method for independent sequences under the framework of sublinear expectation, which transforms a sequence with mean uncertainty into an independent sequence with zero-mean. The related properties of such normalization are obtained. As an application, the necessary and sufficient conditions for the central limit theorem for independent and identically distributed random vectors with mean uncertainty are provided.</p>

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Normalization of independent random variables with mean uncertainty and its application to the central limit theorem under sublinear expectations

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Xinpeng Li,
  • Jingxu Niu,
  • Li-Xin Zhang

摘要

In this paper, we propose a novel normalization method for independent sequences under the framework of sublinear expectation, which transforms a sequence with mean uncertainty into an independent sequence with zero-mean. The related properties of such normalization are obtained. As an application, the necessary and sufficient conditions for the central limit theorem for independent and identically distributed random vectors with mean uncertainty are provided.