A Nonconventional Local Limit Theorem

Yeor Hafouta, Yuri Kifer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Local limit theorems have their origin in the classical De Moivre–Laplace theorem, and they study the asymptotic behavior as N→ ∞ of probabilities having the form P{ SN= k} where SN=∑n=1NF(ξn) is a sum of an integer-valued function F taken on i.i.d. or Markov-dependent sequence of random variables { ξj}. Corresponding results for lattice-valued and general functions F were obtained, as well. We extend here this type of results to nonconventional sums of the form SN=∑n=1NF(ξn,ξ2n,…,ξℓn) which continues the recent line of research studying various limit theorems for such expressions.

Original languageEnglish
Pages (from-to)1524-1553
Number of pages30
JournalJournal of Theoretical Probability
Volume29
Issue number4
DOIs
StatePublished - 1 Dec 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer Science+Business Media New York.

Keywords

  • Local limit theorem
  • Markov chain
  • Mixing
  • Nonconventional setup

Fingerprint

Dive into the research topics of 'A Nonconventional Local Limit Theorem'. Together they form a unique fingerprint.

Cite this