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

Research output: Contribution to journalArticle

### Abstract

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 (Formula presented.) where F is a polynomial, (Formula presented.) is either (Formula presented.) or ni and (Formula presented.) 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).

Original language English (US) 1-34 34 Journal of Statistical Physics https://doi.org/10.1007/s10955-016-1561-5 Accepted/In press - Jun 16 2016

### Fingerprint

random variables
Heavy Tails
Tail
polynomials
Random variable
Polynomial
theorems
Functional Central Limit Theorem
Independent Random Variables
Limit Theorems
Decay Rate
Identically distributed
decay rates

### Keywords

• Heavy tails
• Levi process
• Limit theorems
• Nonconventional sums
• Stable distributions

### ASJC Scopus subject areas

• Statistical and Nonlinear Physics
• Mathematical Physics

### Cite this

Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums. / Kifer, Yuri; Varadhan, Srinivasa.

In: Journal of Statistical Physics, 16.06.2016, p. 1-34.

Research output: Contribution to journalArticle

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