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

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• 作者：Yuri Kifer ; S. R. S. Varadhan
• 关键词：Stable distributions ; Heavy tails ; Limit theorems ; Levi process ; Nonconventional sums
• 刊名：Journal of Statistical Physics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：166
• 期：3-4
• 页码：575-608
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Statistical Physics and Dynamical Systems; Theoretical, Mathematical and Computational Physics; Physical Chemistry; Quantum Physics;
• 出版者：Springer US
• ISSN：1572-9613
• 卷排序：166

文摘

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 \(\sum _{Nt\ge n\ge 1}F\big (X_{q_1(n)},\ldots ,X_{q_\ell (n)}\big )\) where F is a polynomial, \(q_i(n)\) is either \(n-1+i\) or ni and \(X_n,n\ge 0\) 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).