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A quantitative discounted central limit theorem using the Fourier metric

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  • Katriel, Guy

Abstract

The discounted central limit theorem concerns the convergence of an infinite discounted sum of i.i.d. random variables to normality as the discount factor approaches 1. We show that, using the Fourier metric on probability distributions, one can obtain the discounted central limit theorem, as well as a quantitative version of it, in a simple and natural way, and under weak assumptions.

Suggested Citation

  • Katriel, Guy, 2019. "A quantitative discounted central limit theorem using the Fourier metric," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 321-326.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:321-326
    DOI: 10.1016/j.spl.2018.10.013
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    References listed on IDEAS

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    1. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
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