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Seo, Byoung Ki
Trading Engineering Lab
Research Interests
  • Financial Engineering, Finanicial Mathematics, Market Microstructure

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The waiting time for irrational rotations

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Title
The waiting time for irrational rotations
Author
Kim, DHSeo, Byoung Ki
Issue Date
2003-09
Publisher
IOP PUBLISHING LTD
Citation
NONLINEARITY, v.16, no.5, pp.1861 - 1868
Abstract
Let Tx = x + θ (mod 1). Define Kn(x, y) = min{j ≥ 1 : Tjy ∈. Qn(x)}, where Qn(x) = [2 -ni,2-n(i + 1)) for 2-ni ≤ x < 2 -n(i + 1). Then for irrational θ of type η lim inf n→∞log Kn(x, y)/n = 1 a.e., lim sup n→∞log Kn(x, y)/n = η a.e. Since the set of irrational numbers of type 1 has measure 1, for almost every 9 the limit exists and is 1.
URI
https://scholarworks.unist.ac.kr/handle/201301/8805
URL
http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=0142137601
DOI
10.1088/0951-7715/16/5/318
ISSN
0951-7715
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SBA_Journal Papers
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