Local limit theorem in deterministic systems

Zemer Kosloff; Dalibor Volny

doi:10.1214/21-aihp1169

Local limit theorem in deterministic systems

Zemer Kosloff, Dalibor Volny

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

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

Abstract

We show that for every ergodic and aperiodic probability preserving system, there exists an integer valued square integrable function whose Birkhoff sums process satisfies the lattice local limit theorem.

Original language	English
Pages (from-to)	548-566
Number of pages	19
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	58
Issue number	1
DOIs	https://doi.org/10.1214/21-aihp1169
State	Published - Feb 2021

Keywords

Dynamical systems
Local Central Theorem
Zero entropy stationary process

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/21-aihp1169

Cite this

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title = "Local limit theorem in deterministic systems",

abstract = "We show that for every ergodic and aperiodic probability preserving system, there exists an integer valued square integrable function whose Birkhoff sums process satisfies the lattice local limit theorem.",

keywords = "Dynamical systems, Local Central Theorem, Zero entropy stationary process",

author = "Zemer Kosloff and Dalibor Volny",

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N2 - We show that for every ergodic and aperiodic probability preserving system, there exists an integer valued square integrable function whose Birkhoff sums process satisfies the lattice local limit theorem.

AB - We show that for every ergodic and aperiodic probability preserving system, there exists an integer valued square integrable function whose Birkhoff sums process satisfies the lattice local limit theorem.

KW - Dynamical systems

KW - Local Central Theorem

KW - Zero entropy stationary process

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M3 - مقالة

SN - 0246-0203

VL - 58

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JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

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Local limit theorem in deterministic systems

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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