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Forward-convex convergence in probability of sequences of nonnegative random variables

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  • Constantinos Kardaras
  • Gordan Zitkovic

Abstract

For a sequence of nonnegative random variables, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges in probability to the same limit. These conditions correspond to an essentially measure-free version of the notion of uniform integrability.

Suggested Citation

  • Constantinos Kardaras & Gordan Zitkovic, 2010. "Forward-convex convergence in probability of sequences of nonnegative random variables," Papers 1002.1889, arXiv.org, revised Feb 2011.
    • Handle: RePEc:arx:papers:1002.1889
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    File URL: http://arxiv.org/pdf/1002.1889
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    1. Dellacherie, C., 1980. "Un survol de la theorie de l'integrale stochastique," Stochastic Processes and their Applications, Elsevier, vol. 10(2), pages 115-144, September.
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