Abstract Methods In Information Theory (Second Edition) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Abstract Methods In Information Theory (Second Edition) write by Yuichiro Kakihara. This book was released on 2016-06-09. Abstract Methods In Information Theory (Second Edition) available in PDF, EPUB and Kindle. Information Theory is studied from the following points of view: (1) the theory of entropy as amount of information; (2) the mathematical structure of information sources (probability measures); and (3) the theory of information channels. Shannon entropy and Kolmogorov-Sinai entropy are defined and their basic properties are examined, where the latter entropy is extended to be a linear functional on a certain set of measures. Ergodic and mixing properties of stationary sources are studied as well as AMS (asymptotically mean stationary) sources.The main purpose of this book is to present information channels in the environment of functional analysis and operator theory as well as probability theory. Ergodic, mixing, and AMS channels are also considered in detail with some illustrations. In this second edition, channel operators are studied in many aspects, which generalize ordinary channels. Also Gaussian channels are considered in detail together with Gaussian measures on a Hilbert space. The Special Topics chapter deals with features such as generalized capacity, channels with an intermediate noncommutative system, and von Neumann algebra method for channels. Finally, quantum (noncommutative) information channels are examined in an independent chapter, which may be regarded as an introduction to quantum information theory. Von Neumann entropy is introduced and its generalization to a C*-algebra setting is given. Basic results on quantum channels and entropy transmission are also considered.
Abstract Methods in Information Theory
Abstract Methods in Information Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Abstract Methods in Information Theory write by Yichir Kakihara. This book was released on 1999. Abstract Methods in Information Theory available in PDF, EPUB and Kindle. Information Theory is studied from the following view points: (1) the theory of entropy as amount of information; (2) the mathematical structure of information sources (probability measures); and (3) the theory of information channels. Shannon entropy and Kolmogorov-Sinai entropy are defined and their basic properties are examined, where the latter entropy is extended to be a linear functional on a certain set of measures. Ergodic and mixing properties of stationary sources are studied as well as AMS (asymptotically mean stationary) sources. The main purpose of this book is to present information channels in the environment of real and functional analysis as well as probability theory. Ergodic channels are characterized in various manners. Mixing and AMS channels are also considered in detail with some illustrations. A few other aspects of information channels including measurability, approximation and noncommutative extensions, are also discussed.
Stochastic Processes: Harmonizable Theory
Stochastic Processes: Harmonizable Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Processes: Harmonizable Theory write by Malempati Madhusudana Rao. This book was released on 2020-09-21. Stochastic Processes: Harmonizable Theory available in PDF, EPUB and Kindle. The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These include Levy's Brownian motion, a probabilistic proof of the longstanding Riemann's hypothesis, random fields indexed by LCA and hypergroups, extensions to bistochastic operators, Cramér-Karhunen classes, as well as bistochastic operators with some statistical applications.The material is accessible to graduate students in probability and statistics as well as to engineers in theoretical applications. There are numerous extensions and applications pointed out in the book that will inspire readers to delve deeper.
Hilbert And Banach Space-valued Stochastic Processes
Hilbert And Banach Space-valued Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hilbert And Banach Space-valued Stochastic Processes write by Yuichiro Kakihara. This book was released on 2021-07-29. Hilbert And Banach Space-valued Stochastic Processes available in PDF, EPUB and Kindle. This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ≥ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.
Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences
Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences write by Rupert Lasser. This book was released on 2022-12-06. Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences available in PDF, EPUB and Kindle. The book aims at giving a monographic presentation of the abstract harmonic analysis of hypergroups, while combining it with applied topics of spectral analysis, approximation by orthogonal expansions and stochastic sequences. Hypergroups are locally compact Hausdorff spaces equipped with a convolution, an involution and a unit element. Related algebraic structures had already been studied by Frobenius around 1900. Their axiomatic characterisation in harmonic analysis was later developed in the 1970s. Hypergoups naturally emerge in seemingly different application areas as time series analysis, probability theory and theoretical physics.The book presents harmonic analysis on commutative and polynomial hypergroups as well as weakly stationary random fields and sequences thereon. For polynomial hypergroups also difference equations and stationary sequences are considered. At greater extent than in the existing literature, the book compiles a rather comprehensive list of hypergroups, in particular of polynomial hypergroups. With an eye on readers at advanced undergraduate and graduate level, the proofs are generally worked out in careful detail. The bibliography is extensive.
