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 ∑Nt≥n≥1F(Xq1(n),…,Xqℓ(n)) where F is a polynomial, qi(n) is either n- 1 + i or ni and Xn, n≥ 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).
Original language | English |
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Pages (from-to) | 575-608 |
Number of pages | 34 |
Journal | Journal of Statistical Physics |
Volume | 166 |
Issue number | 3-4 |
DOIs | |
State | Published - 1 Feb 2017 |
Bibliographical note
Publisher Copyright:© 2016, Springer Science+Business Media New York.
Keywords
- Heavy tails
- Levi process
- Limit theorems
- Nonconventional sums
- Stable distributions