On the discrepancy of random subsequences of {nα}, II

István Berkes; Bence Borda

doi:10.4064/aa200811-25-1

On the discrepancy of random subsequences of {nα}, II

István Berkes, Bence Borda

Institute of Analysis and Number Theory (5010)

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

Abstract

Let α be an irrational number, let X1,X2,… be independent, identically distributed, integer-valued random variables, and put Sk=∑kj=1Xj. Assuming that X1 has finite variance or heavy tails P(|X1|>t)∼ct−β, 0

Original language	English
Pages (from-to)	303-330
Number of pages	28
Journal	Acta Arithmetica
Volume	199
Issue number	3
DOIs	https://doi.org/10.4064/aa200811-25-1
Publication status	Published - 2021

Keywords

Diophantine approximation
discrepancy
functional limit theorems
nonstationary process
random walk

ASJC Scopus subject areas

Algebra and Number Theory

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10.4064/aa200811-25-1

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abstract = "Let α be an irrational number, let X1,X2,… be independent, identically distributed, integer-valued random variables, and put Sk=∑kj=1Xj. Assuming that X1 has finite variance or heavy tails P(|X1|>t)∼ct−β, 0",

keywords = "Diophantine approximation, discrepancy, functional limit theorems, nonstationary process, random walk",

author = "Istv{\'a}n Berkes and Bence Borda",

note = "Funding Information: Acknowledgments. Research of I. B. was supported by NKFIH grant K 125569. Funding Information: Research of B. B. was supported by the Austrian Science Fund (FWF), project Y-901.",

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N2 - Let α be an irrational number, let X1,X2,… be independent, identically distributed, integer-valued random variables, and put Sk=∑kj=1Xj. Assuming that X1 has finite variance or heavy tails P(|X1|>t)∼ct−β, 0

AB - Let α be an irrational number, let X1,X2,… be independent, identically distributed, integer-valued random variables, and put Sk=∑kj=1Xj. Assuming that X1 has finite variance or heavy tails P(|X1|>t)∼ct−β, 0

KW - Diophantine approximation

KW - discrepancy

KW - functional limit theorems

KW - nonstationary process

KW - random walk

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On the discrepancy of random subsequences of {nα}, II

Abstract

Keywords

ASJC Scopus subject areas

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