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From Classical to Modern Nonlinear Central Limit Theorems

Author

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  • Vladimir V. Ulyanov

    (Faculty of Computer Science, HSE University, 109028 Moscow, Russia
    Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia)

Abstract

In 1733, de Moivre, investigating the limit distribution of the binomial distribution, was the first to discover the existence of the normal distribution and the central limit theorem (CLT). In this review article, we briefly recall the history of classical CLT and martingale CLT, and introduce new directions of CLT, namely Peng’s nonlinear CLT and Chen–Epstein’s nonlinear CLT, as well as Chen–Epstein’s nonlinear normal distribution function.

Suggested Citation

  • Vladimir V. Ulyanov, 2024. "From Classical to Modern Nonlinear Central Limit Theorems," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2276-:d:1439601
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    References listed on IDEAS

    as
    1. Chen, Zengjing & Epstein, Larry G. & Zhang, Guodong, 2023. "A central limit theorem, loss aversion and multi-armed bandits," Journal of Economic Theory, Elsevier, vol. 209(C).
    2. Chen, Zengjing & Epstein, Larry G., 2022. "A central limit theorem for sets of probability measures," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 424-451.
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