Information theoretic properties of stochastic processes on partition fibers

dc.creatorOliveira, Luiz Eugenio Barboza de
dc.date.accessioned2021-12-14T19:39:02Z
dc.date.available2021-12-14T19:39:02Z
dc.date.issued1975
dc.description.abstractIn a probability space, the partition fiber relative to a probability vector v is the set of all ordered partitions of that space, the probabilities of whose atoms are the components of v. We define as an stochastic process any ordered pair consisting of a measure preserving transformation of the probability space, and an ordered finite partition of this space. To each stochastic process one assigns the usual Kolmogorov-Sinai relative entropy. The main result of this dissertation is that for each ergodic measure preserving invertible transformation T of an atomless probability space, and for each probability vector v, there are ordered partitiers in the partition fiber relative to v.such that the relative entropy on the resulting stochastic processes assumes any value between zero an the least of H(v) and h(T). This result is arrived at by generalizing to atomless spaces techniques used by D.S.Ornstein in [1970-Ornstein].
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other2211062
dc.identifier.urihttps://hdl.handle.net/10657/8357
dc.language.isoen
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleInformation theoretic properties of stochastic processes on partition fibers
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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