Rates of Convergence in Laplace's Integrals and Sums and Conditional Central Limit Theorems

被引：1
作者：
Kolokoltsov, Vassili N. [1 ]
机构：
[1] Univ Warwick, Dept Stat, Coventry CV4 7AL, W Midlands, England
来源：
MATHEMATICS | 2020年 / 8卷 / 04期
关键词：
integrals and sums; rates of convergence; conditional law of large numbers; conditional central limit theorem; ASYMPTOTICS; WELL; LAW;
D O I：
10.3390/math8040479
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We obtained the exact estimates for the error terms in Laplace's integrals and sums implying the corresponding estimates for the related laws of large number and central limit theorems including the large deviations approximation.
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页数：19
相关论文
共 18 条
[1]   Asymptotics of Gaussian integrals in infinite dimensions [J].
Albeverio, Sergio ;
Steblovskaya, Victoria .
INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 2019, 22 (01)
[2]  
[Anonymous], 2009, STAT MECH QUANTUM LA
[3]  
Borovkov A.A., 1965, TEOR VEROJATNOST PRI, V10, P61
[4]   A NOTE ON THE NON-COMMUTATIVE LAPLACE-VARADHAN INTEGRAL LEMMA [J].
De Roeck, W. ;
Maes, Christian ;
Netocny, Karel ;
Rey-Bellet, Luc .
REVIEWS IN MATHEMATICAL PHYSICS, 2010, 22 (07) :839-858
[5]   A note on the Laplace-Varadhan integral lemma [J].
Del Moral, P ;
Zajic, T .
BERNOULLI, 2003, 9 (01) :49-65
[6]   THE DOUBLE-WELL SPLITTING OF THE LOW-ENERGY LEVELS FOR THE SCHRODINGER OPERATOR OF DISCRETE PHI-4-MODELS ON TORI [J].
DOBROKHOTOV, SY ;
KOLOKOLTSOV, VN .
JOURNAL OF MATHEMATICAL PHYSICS, 1995, 36 (03) :1038-1053
[7]  
Grenander Ulf., 1981, Lectures in Pattern Theory, Volume 3: Regular Structures, V3
[8]  
Kolokoltsov V. N, 2000, SEMICLASSICAL ANAL D, V1724
[9]  
Kolokoltsov V.N., 2019, DIFF EQUAT+
[10]  
KOLOKOLTSOV VN, 1993, DOKL AKAD NAUK+, V328, P649
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