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On uniform nonintegrability for a sequence of random variables

Author

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  • Chandra, Tapas K.
  • Hu, Tien-Chung
  • Rosalsky, Andrew

Abstract

In this correspondence, we introduce the notion of a sequence of random variables being uniformly nonintegrable. Sufficient and, separately, necessary conditions for uniform nonintegrability are presented and we also establish two equivalent characterizations of uniform nonintegrability, one of which is a uniform nonintegrability analogue of the celebrated de La Vallée Poussin criterion for uniform integrability. Several illustrative examples are presented.

Suggested Citation

  • Chandra, Tapas K. & Hu, Tien-Chung & Rosalsky, Andrew, 2016. "On uniform nonintegrability for a sequence of random variables," Statistics & Probability Letters, Elsevier, vol. 116(C), pages 27-37.
    • Handle: RePEc:eee:stapro:v:116:y:2016:i:c:p:27-37
    DOI: 10.1016/j.spl.2016.04.015
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    References listed on IDEAS

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    1. Hu, Tien-Chung & Rosalsky, Andrew, 2011. "A note on the de La Vallée Poussin criterion for uniform integrability," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 169-174, January.
    2. Chandra, Tapas Kumar, 2015. "de La Vallée Poussin’s theorem, uniform integrability, tightness and moments," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 136-141.
    3. Hu, Tien-Chung & Rosalsky, Andrew, 2015. "A note on random variables with an infinite absolute first moment," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 212-215.
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