A WEAK LAW OF LARGE NUMBERS FOR DEPENDENT RANDOM VARIABLES

被引：1

作者：

Karatzas, I. ^{[1
,2
]}

Schachermayer, W. ^{[3
]}

机构：

[1] Columbia Univ, Dept Math, New York, NY 10027 USA

[2] Columbia Univ, Dept Stat, New York, NY 10027 USA

[3] Univ Vienna, Fac Math, Vienna, Austria

来源：

THEORY OF PROBABILITY AND ITS APPLICATIONS | 2023年 / 68卷 / 03期

基金：

美国国家科学基金会; 奥地利科学基金会;

关键词：

weak law of large numbers; hereditary convergence; weak convergence; truncation; generalized expectation; nonlinear expectation;

D O I：

10.1137/S0040585X97T991593

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Each sequence f(1), f(2),... of random variables satisfying lim(M ->infinity)(M sup(k is an element of N)P(vertical bar f(k)vertical bar > M)) = 0 contains a subsequence f(k1), f(k2), ... which, along with all its subsequences, satisfies the weak law of large numbers lim(N ->infinity) ((1/N) Sigma(N)(n=1) f(kn) - D-N) = 0 in probability. Here, DN is a "corrector" random variable with values in [-N, N] for each N is an element of N; these correctors are all equal to zero if, in addition, lim inf(n ->infinity) E(f(n)(2) 1({broken vertical bar fn broken vertical bar <= M})) = 0 for every M is an element of (0, infinity).

引用

页码：501 / 509

页数：9

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