dc.contributor.advisor Nicol, Matthew dc.creator Zhang, Licheng 1987- dc.date.accessioned 2017-06-12T21:22:54Z dc.date.available 2017-06-12T21:22:54Z dc.date.created May 2015 dc.date.issued 2015-05 dc.date.submitted May 2015 dc.identifier.citation Portions 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.uri http://hdl.handle.net/10657/1771 dc.description.abstract In 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.mimetype application/pdf dc.language.iso eng dc.subject Central limit theorem dc.subject Borel-Cantelli Lemma dc.subject Lorenz system dc.subject Extreme Value theory dc.title Statistical Properties of Chaotic Dynamical Systems: Non-Stationary Central Limit Theorems and Extreme Value Theory dc.date.updated 2017-06-12T21:22:55Z dc.type.genre Thesis thesis.degree.name Doctor of Philosophy thesis.degree.level Doctoral thesis.degree.discipline Mathematics thesis.degree.grantor University of Houston dc.contributor.committeeMember Zhang, Hongkun dc.contributor.committeeMember Török, Andrew dc.contributor.committeeMember Gunaratne, Gemunu H. dc.type.dcmi text dc.format.digitalOrigin born digital dc.description.department Mathematics thesis.degree.college College of Natural Sciences and Mathematics
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