Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums

被引：2

作者：

Kifer, Yuri ^{[1
]}

Varadhan, S. R. S. ^{[2
]}

机构：

[1] Hebrew Univ Jerusalem, Inst Math, IL-91904 Jerusalem, Israel

[2] NYU, Courant Inst Math Studies, 251 Mercer St, New York, NY 10012 USA

来源：

JOURNAL OF STATISTICAL PHYSICS | 2017年 / 166卷 / 3-4期

基金：

以色列科学基金会; 美国国家科学基金会;

关键词：

Stable distributions; Heavy tails; Limit theorems; Levi process; Nonconventional sums; THEOREMS;

D O I：

10.1007/s10955-016-1561-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

First, we obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails. Then we derive stable limit theorems for sums of the form where F is a polynomial, is either or ni and is a sequence of independent identically distributed random variables with heavy tails. Our results can be viewed as an extension to the heavy tails case of the nonconventional functional central limit theorem from Kifer and Varadhan (Ann Probab 42:649-688, 2014).

引用

页码：575 / 608

页数：34

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