### 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) |
---|---|

Pages (from-to) | 1-34 |

Number of pages | 34 |

Journal | Journal of Statistical Physics |

DOIs | |

State | Accepted/In press - Jun 16 2016 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Journal of Statistical Physics*, 1-34. https://doi.org/10.1007/s10955-016-1561-5

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

Research output: Contribution to journal › Article

*Journal of Statistical Physics*, pp. 1-34. https://doi.org/10.1007/s10955-016-1561-5

}

TY - JOUR

T1 - Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums

AU - Kifer, Yuri

AU - Varadhan, Srinivasa

PY - 2016/6/16

Y1 - 2016/6/16

N2 - 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).

AB - 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).

KW - Heavy tails

KW - Levi process

KW - Limit theorems

KW - Nonconventional sums

KW - Stable distributions

UR - http://www.scopus.com/inward/record.url?scp=84975110718&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975110718&partnerID=8YFLogxK

U2 - 10.1007/s10955-016-1561-5

DO - 10.1007/s10955-016-1561-5

M3 - Article

AN - SCOPUS:84975110718

SP - 1

EP - 34

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

ER -