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

Yuri Kifer, S. R.S. Varadhan

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 ∑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 languageEnglish (US)
Pages (from-to)575-608
Number of pages34
JournalJournal of Statistical Physics
Volume166
Issue number3-4
DOIs
StatePublished - 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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