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Two inequalities for conditional expectations and convergence results for filters

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  • Crimaldi, Irene
  • Pratelli, Luca

Abstract

In this paper we prove, first of all, two inequalities for conditional expectations, from which we easily deduce a result by Landers and Rogge. Then we prove convergence results for conditional expectations of the form Pn[f(Xn)Yn] to a conditional expectation of the form P[f(X)Y]. We study, in particular, the case in which the random variables are of the type .

Suggested Citation

  • Crimaldi, Irene & Pratelli, Luca, 2005. "Two inequalities for conditional expectations and convergence results for filters," Statistics & Probability Letters, Elsevier, vol. 74(2), pages 151-162, September.
    • Handle: RePEc:eee:stapro:v:74:y:2005:i:2:p:151-162
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    Cited by:

    1. Camargo, Braz, 2014. "Learning in society," Games and Economic Behavior, Elsevier, vol. 87(C), pages 381-396.
    2. Luca Pratelli & Pietro Rigo, 2023. "A Strong Version of the Skorohod Representation Theorem," Journal of Theoretical Probability, Springer, vol. 36(1), pages 372-389, March.
    3. Pooya Molavi & Ceyhun Eksin & Alejandro Ribeiro & Ali Jadbabaie, 2016. "Learning to Coordinate in Social Networks," Operations Research, INFORMS, vol. 64(3), pages 605-621, June.
    4. Patrizia Berti & Luca Pratelli & Pietro Rigo, 2021. "A Central Limit Theorem for Predictive Distributions," Mathematics, MDPI, vol. 9(24), pages 1-11, December.

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