From Classical to Modern Nonlinear Central Limit Theorems

被引：2
作者：
Ulyanov, Vladimir V. [1 ,2 ]
机构：
[1] HSE Univ, Fac Comp Sci, Moscow 109028, Russia
[2] Lomonosov Moscow State Univ, Fac Computat Math & Cybernet, Moscow 119991, Russia
来源：
MATHEMATICS | 2024年 / 12卷 / 14期
关键词：
central limit theorem; martingale CLT; nonlinear Peng's CLT; nonlinear Chen-Epstein CLT; RATES; CLT;
D O I：
10.3390/math12142276
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页数：17
相关论文
共 41 条
[1]  
Adams W.J., 2009, History of Mathematics, Volume 35
[2]  
[Anonymous], 1738, The Doctrine of Chances
[3]  
[Anonymous], 1809, Theoria motus corporum coelestium in sectionibus conicis Solem ambientium
[4]  
[Anonymous], 1961, Proc. Am. Math. Soc., DOI DOI 10.2307/2034876
[5]  
[Anonymous], 1995, Limit Theorems of Probability Theory: Sequences of Independent Random Variables, DOI DOI 10.1214/08-EJS176
[6]  
[Anonymous], 1953, Stochastic Processes
[7]  
Bentkus V, 1996, ANN PROBAB, V24, P466
[8]   The extension of the limited theorem of calculus in the probabilities of sums of independent quantities [J].
Bernstein, S .
MATHEMATISCHE ANNALEN, 1927, 97 :1-59
[9]  
Bhattacharya R.N., 1976, Wiley Ser. Probab. Math. Statist.
[10]   MARTINGALE CENTRAL LIMIT THEOREMS [J].
BROWN, BM .
ANNALS OF MATHEMATICAL STATISTICS, 1971, 42 (01) :59-&
12345