Affiliation:
1. Faculty of Computer Science, HSE University, 109028 Moscow, Russia
2. 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.
Reference41 articles.
1. On the Functional Central Limit Theorem for Martingales;Z. Wahrscheinlichkeitstheorie Verw. Geb.,1977
2. Hall, P., and Heyde, C.C. (1980). Martingale Limit Theory and Its Application, Academic Press.
3. Adams, W.J. (2009). The Life and Times of the Central Limit Theorem, 2nd ed. History of Mathematics, Volume 35, American Mathematical Society.
4. Fischer, H. (2011). A History of the Central Limit Theorem, From Classical to Modern Probability Theory, Springer.
5. Petrov, V.V. (1995). Limit Theorems of Probability Theory, Oxford Science Publications.