Nonconventional limit theorems in averaging

Yuri Kifer

doi:10.1214/12-AIHP514

Nonconventional limit theorems in averaging

Yuri Kifer^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider "nonconventional" averaging setup in the form {equation presented} where (t), t ≥ 0 is either a stochastic process or a dynamical system with sufficiently fast mixing while q_j (t) = α_jt, α₁ < α₂ < . . . < α_k and q_j, j = k + 1, . . . , l grow faster than linearly. We show that the properly normalized error term in the "nonconventional" averaging principle is asymptotically Gaussian.

Original language	English
Pages (from-to)	236-255
Number of pages	20
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	50
Issue number	1
DOIs	https://doi.org/10.1214/12-AIHP514
State	Published - Feb 2014

Keywords

Averaging
Hyperbolic dynamical systems
Limit theorems
Martingales

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10.1214/12-AIHP514

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KW - Martingales

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Nonconventional limit theorems in averaging

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Keywords

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