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 language | English |
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Pages (from-to) | 1524-1553 |
Number of pages | 30 |
Journal | Journal of Theoretical Probability |
Volume | 29 |
Issue number | 4 |
DOIs | |
State | Published - 1 Dec 2016 |
Bibliographical note
Publisher Copyright:© 2015, Springer Science+Business Media New York.
Keywords
- Local limit theorem
- Markov chain
- Mixing
- Nonconventional setup