From Classical to Modern Nonlinear Central Limit Theorems

Vladimir V. Ulyanov ()
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Vladimir V. Ulyanov: Faculty of Computer Science, HSE University, 109028 Moscow, Russia

Mathematics, 2024, vol. 12, issue 14, 1-17

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.

Keywords: central limit theorem; martingale CLT; nonlinear Peng’s CLT; nonlinear Chen—Epstein CLT (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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