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A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers

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  • Castaing, Charles
  • Quang, Nguyen Van
  • Thuan, Nguyen Tran

Abstract

We consider a new family of convex weakly compact valued integrable random sets which is called an adapted array of convex weakly compact valued integrable random variables of type p (1⩽p⩽2). By this concept, more general laws of large numbers will be established. Some illustrative examples are provided.

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  • Castaing, Charles & Quang, Nguyen Van & Thuan, Nguyen Tran, 2012. "A new family of convex weakly compact valued random variables in Banach space and applications to laws of large numbers," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 84-95.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:84-95
    DOI: 10.1016/j.spl.2011.08.012
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    References listed on IDEAS

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    1. Quang, Nguyen Van & Huan, Nguyen Van, 2009. "On the strong law of large numbers and -convergence for double arrays of random elements in p-uniformly smooth Banach spaces," Statistics & Probability Letters, Elsevier, vol. 79(18), pages 1891-1899, September.
    2. Hiai, Fumio & Umegaki, Hisaharu, 1977. "Integrals, conditional expectations, and martingales of multivalued functions," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 149-182, March.
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    Cited by:

    1. Quang, Nguyen Van & Giap, Duong Xuan, 2013. "Mosco convergence of SLLN for triangular arrays of rowwise independent random sets," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1117-1126.

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