Limit Theorems for Non-stationary and Random Dynamical Systems

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dc.contributor.advisorTörök, Andrew
dc.contributor.committeeMemberClimenhaga, Vaughn
dc.contributor.committeeMemberNicol, Matthew
dc.contributor.committeeMemberGunaratne, Gemunu H.
dc.creatorSu, Yaofeng
dc.date.accessioned2020-06-02T04:48:58Z
dc.date.available2020-06-02T04:48:58Z
dc.date.createdMay 2020
dc.date.issued2020-05
dc.date.submittedMay 2020
dc.date.updated2020-06-02T04:48:58Z
dc.description.abstractWe study the limit behavior of non-stationary/random chaotic dynamical systems and prove a strong statistical limit theorem: (vector-valued) almost sure invariance principle for non-stationary dynamical systems and quenched (vector-valued) almost sure invariance principle for random dynamical systems. It is a matching of the trajectories of the dynamical system with a Brownian motion in such a way that the error is negligible in comparison with the Birkhoff sum. We develop a method called "reverse Gaussian approximation" and apply it to the classical block construction. We apply our results to the stationary chaotic systems which can be described by Young tower, and the (non)uniformly expanding non-stationary/random dynamical systems with intermittency or uniform spectral gap. Our results imply that the systems we study have many limit results that are satisfied by Brownian motion.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10657/6611
dc.language.isoeng
dc.rightsThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).
dc.subjectalmost sure invariance principle, non-stationary dynamical system, random dynamical system, decay of correlation
dc.titleLimit Theorems for Non-stationary and Random Dynamical Systems
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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