### 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, q_{i}(n) is either n- 1 + i or ni and X_{n}, 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 (US) |
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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 - Feb 1 2017 |

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Kifer, Y., & Varadhan, S. R. S. (2017). Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums.

*Journal of Statistical Physics*,*166*(3-4), 575-608. https://doi.org/10.1007/s10955-016-1561-5