Structural Aspects In The Theory Of Probability A Primer In Probabilities On Algebraic Topological Structures

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Structural Aspects in the Theory of Probability

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Author : Herbert Heyer
Publisher : World Scientific
ISBN 13 : 9812562281
Total Pages : 399 pages
Book Rating : 4.8/5 (125 download)

Book Synopsis Structural Aspects in the Theory of Probability by : Herbert Heyer

Download or read book Structural Aspects in the Theory of Probability written by Herbert Heyer and published by World Scientific. This book was released on 2004 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the algebraic-topological aspects of probabilitytheory, leading to a wider and deeper understanding of basic theorems, such as those on the structure of continuous convolution semigroupsand the corresponding processes with independent increments

Structural Aspects in the Theory of Probability

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Author : Herbert Heyer
Publisher : World Scientific
ISBN 13 : 9814282480
Total Pages : 425 pages
Book Rating : 4.8/5 (142 download)

Book Synopsis Structural Aspects in the Theory of Probability by : Herbert Heyer

Download or read book Structural Aspects in the Theory of Probability written by Herbert Heyer and published by World Scientific. This book was released on 2010 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is conceived as a text accompanying the traditional graduate courses on probability theory. An important feature of this enlarged version is the emphasis on algebraic-topological aspects leading to a wider and deeper understanding of basic theorems such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. Fourier transformation ? the method applied within the settings of Banach spaces, locally compact Abelian groups and commutative hypergroups ? is given an in-depth discussion. This powerful analytic tool along with the relevant facts of harmonic analysis make it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. In extension of the first edition, the new edition contains chapters on the probability theory of generalized convolution structures such as polynomial and Sturm?Liouville hypergroups, and on the central limit problem for groups such as tori, p-adic groups and solenoids.

Structural Aspects in the Theory of Probability

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Author :
Publisher :
ISBN 13 : 9814466948
Total Pages : pages
Book Rating : 4.8/5 (144 download)

Book Synopsis Structural Aspects in the Theory of Probability by :

Download or read book Structural Aspects in the Theory of Probability written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Structural Aspects In The Theory Of Probability: A Primer In Probabilities On Algebraic - Topological Structures

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Author : Herbert Heyer
Publisher : World Scientific
ISBN 13 : 981448217X
Total Pages : 399 pages
Book Rating : 4.8/5 (144 download)

Book Synopsis Structural Aspects In The Theory Of Probability: A Primer In Probabilities On Algebraic - Topological Structures by : Herbert Heyer

Download or read book Structural Aspects In The Theory Of Probability: A Primer In Probabilities On Algebraic - Topological Structures written by Herbert Heyer and published by World Scientific. This book was released on 2004-08-23 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the algebraic-topological aspects of probability theory, leading to a wider and deeper understanding of basic theorems, such as those on the structure of continuous convolution semigroups and the corresponding processes with independent increments. The method applied within the setting of Banach spaces and of locally compact Abelian groups is that of the Fourier transform. This analytic tool along with the relevant parts of harmonic analysis makes it possible to study certain properties of stochastic processes in dependence of the algebraic-topological structure of their state spaces. Graduate students, lecturers and researchers may use the book as a primer in the theory of probability measures on groups and related structures.This book has been selected for coverage in:• CC / Physical, Chemical & Earth Sciences• Index to Scientific Book Contents® (ISBC)

Noncommutative Analysis, Operator Theory and Applications

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Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3319291165
Total Pages : 283 pages
Book Rating : 4.3/5 (192 download)

Book Synopsis Noncommutative Analysis, Operator Theory and Applications by : Daniel Alpay

Download or read book Noncommutative Analysis, Operator Theory and Applications written by Daniel Alpay and published by Birkhäuser. This book was released on 2016-06-30 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

Stochastic Processes: Harmonizable Theory

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Author : Malempati Madhusudana Rao
Publisher : World Scientific
ISBN 13 : 9811213674
Total Pages : 341 pages
Book Rating : 4.8/5 (112 download)

Book Synopsis Stochastic Processes: Harmonizable Theory by : Malempati Madhusudana Rao

Download or read book Stochastic Processes: Harmonizable Theory written by Malempati Madhusudana Rao and published by World Scientific. This book was released on 2020-09-21 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Abstract Methods in Information Theory

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Author : Yûichirô Kakihara
Publisher : World Scientific
ISBN 13 : 9814759252
Total Pages : 412 pages
Book Rating : 4.8/5 (147 download)

Book Synopsis Abstract Methods in Information Theory by : Yûichirô Kakihara

Download or read book Abstract Methods in Information Theory written by Yûichirô Kakihara and published by World Scientific. This book was released on 2016-06-09 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:EntropyInformation SourcesInformation ChannelsChannel OperatorsGaussian ChannelsSpecial TopicsQuantum ChannelsReferencesGlossaries of AxiomsIndices Readership: Graduate students and researchers from Mathematics and Communication Engineering.

Invariant Probabilities of Transition Functions

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Author : Radu Zaharopol
Publisher : Springer
ISBN 13 : 3319057235
Total Pages : 405 pages
Book Rating : 4.3/5 (19 download)

Book Synopsis Invariant Probabilities of Transition Functions by : Radu Zaharopol

Download or read book Invariant Probabilities of Transition Functions written by Radu Zaharopol and published by Springer. This book was released on 2014-06-27 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizations of the supports of various types of invariant probability measures and the use of these to obtain criteria for unique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will be of interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also find this book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, general topology, measure theory, the Bochner integral and some of its applications.

Hilbert And Banach Space-valued Stochastic Processes

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Author : Yuichiro Kakihara
Publisher : World Scientific
ISBN 13 : 9811211760
Total Pages : 539 pages
Book Rating : 4.8/5 (112 download)

Book Synopsis Hilbert And Banach Space-valued Stochastic Processes by : Yuichiro Kakihara

Download or read book Hilbert And Banach Space-valued Stochastic Processes written by Yuichiro Kakihara and published by World Scientific. This book was released on 2021-07-29 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

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Author : Rupert Lasser
Publisher : World Scientific
ISBN 13 : 9811266212
Total Pages : 621 pages
Book Rating : 4.8/5 (112 download)

Book Synopsis Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences by : Rupert Lasser

Download or read book Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences written by Rupert Lasser and published by World Scientific. This book was released on 2022-12-06 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Linear Models And Regression With R: An Integrated Approach

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Author : Debasis Sengupta
Publisher : World Scientific
ISBN 13 : 9811200424
Total Pages : 773 pages
Book Rating : 4.8/5 (112 download)

Book Synopsis Linear Models And Regression With R: An Integrated Approach by : Debasis Sengupta

Download or read book Linear Models And Regression With R: An Integrated Approach written by Debasis Sengupta and published by World Scientific. This book was released on 2019-07-30 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with the basic linear model where the design and covariance matrices are of full rank, this book demonstrates how the same statistical ideas can be used to explore the more general linear model with rank-deficient design and/or covariance matrices. The unified treatment presented here provides a clearer understanding of the general linear model from a statistical perspective, thus avoiding the complex matrix-algebraic arguments that are often used in the rank-deficient case. Elegant geometric arguments are used as needed.The book has a very broad coverage, from illustrative practical examples in Regression and Analysis of Variance alongside their implementation using R, to providing comprehensive theory of the general linear model with 181 worked-out examples, 227 exercises with solutions, 152 exercises without solutions (so that they may be used as assignments in a course), and 320 up-to-date references.This completely updated and new edition of Linear Models: An Integrated Approach includes the following features:

Random and Vector Measures

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Author : Malempati Madhusudana Rao
Publisher : World Scientific
ISBN 13 : 9814350818
Total Pages : 553 pages
Book Rating : 4.8/5 (143 download)

Book Synopsis Random and Vector Measures by : Malempati Madhusudana Rao

Download or read book Random and Vector Measures written by Malempati Madhusudana Rao and published by World Scientific. This book was released on 2012 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deals with the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. This book analyzes several stationary aspects and related processes.

Proceedings of the Fourth German-Japanese Symposium, Infinite Dimensional Harmonic Analysis IV

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Author : Joachim Hilgert
Publisher : World Scientific
ISBN 13 : 9812832823
Total Pages : 337 pages
Book Rating : 4.8/5 (128 download)

Book Synopsis Proceedings of the Fourth German-Japanese Symposium, Infinite Dimensional Harmonic Analysis IV by : Joachim Hilgert

Download or read book Proceedings of the Fourth German-Japanese Symposium, Infinite Dimensional Harmonic Analysis IV written by Joachim Hilgert and published by World Scientific. This book was released on 2009 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourth Conference on Infinite Dimensional Harmonic Analysis brought together experts in harmonic analysis, operator algebras and probability theory. Most of the articles deal with the limit behavior of systems with many degrees of freedom in the presence of symmetry constraints. This volume gives new directions in research bringing together probability theory and representation theory.

Séminaire de Probabilités XLII

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Author : Catherine Donati-Martin
Publisher : Springer
ISBN 13 : 3642017630
Total Pages : 449 pages
Book Rating : 4.6/5 (42 download)

Book Synopsis Séminaire de Probabilités XLII by : Catherine Donati-Martin

Download or read book Séminaire de Probabilités XLII written by Catherine Donati-Martin and published by Springer. This book was released on 2009-06-29 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to rough paths. Coverage also includes the interface between analysis and probability to special processes, Lévy processes and Lévy systems, representation of Gaussian processes, filtrations and quantum probability.

Mathematical Reviews

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Author :
Publisher :
ISBN 13 :
Total Pages : 940 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 940 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Probabilities on Algebraic Structures

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Author : Ulf Grenander
Publisher : Courier Corporation
ISBN 13 : 0486462870
Total Pages : 222 pages
Book Rating : 4.4/5 (864 download)

Book Synopsis Probabilities on Algebraic Structures by : Ulf Grenander

Download or read book Probabilities on Algebraic Structures written by Ulf Grenander and published by Courier Corporation. This book was released on 2008-01-01 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This systematic approach covers semi-groups, groups, linear vector spaces, and algebra. It states and studies fundamental probabilistic problems for these spaces, focusing on concrete results. 1963 edition.

Probabilities on Algebraic Structures

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Author : Ulf Granander
Publisher :
ISBN 13 :
Total Pages : 218 pages
Book Rating : 4.:/5 (63 download)

Book Synopsis Probabilities on Algebraic Structures by : Ulf Granander

Download or read book Probabilities on Algebraic Structures written by Ulf Granander and published by . This book was released on 2008 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: