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dc.contributor.advisorNicol, Matthew
dc.creatorZhang, Licheng 1987-
dc.date.accessioned2017-06-12T21:22:54Z
dc.date.available2017-06-12T21:22:54Z
dc.date.createdMay 2015
dc.date.issued2015-05
dc.date.submittedMay 2015
dc.identifier.citationPortions of this document appear in: Haydn, N., Nicol, M., Vaienti, S., and Zhang, L. (2013). Central limit theorems for the shrinking target problem. Journal of Statistical Physics, 153(5), 864-887.
dc.identifier.urihttp://hdl.handle.net/10657/1771
dc.description.abstractIn this thesis, some statistical properties of two interesting problems are studied. The first one is about non-stationary central limit theorems. We establish central limit theorems for a sequence of nested balls using martingale difference array technique, under certain conditions. It applies to various dynamical systems, including smooth expanding maps of the interval, Rychlik type maps, Gibbs-Markov maps, rational maps, and piecewise expanding maps in higher dimension. And the second problem is about the Lorenz Systems. We study a family of Geometrical Lorenz Models, which have very similar properties to Lorenz Systems and are easier to study. Based on the model, we establish dynamical Borel Cantelli lemmas and convergence of rare event points processes to Poisson processes, which implies Extreme Value Theory.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.subjectCentral limit theorem
dc.subjectBorel-Cantelli Lemma
dc.subjectLorenz system
dc.subjectExtreme Value theory
dc.titleStatistical Properties of Chaotic Dynamical Systems: Non-Stationary Central Limit Theorems and Extreme Value Theory
dc.date.updated2017-06-12T21:22:55Z
dc.type.genreThesis
thesis.degree.nameDoctor of Philosophy
thesis.degree.levelDoctoral
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
dc.contributor.committeeMemberZhang, Hongkun
dc.contributor.committeeMemberTorok, Andrew
dc.contributor.committeeMemberGunaratne, Gemunu H.
dc.type.dcmitext
dc.format.digitalOriginborn digital
dc.description.departmentMathematics
thesis.degree.collegeCollege of Natural Sciences and Mathematics


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