Multidimensional Second Order Stochastic Processes Second Edition
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Multidimensional Second Order Stochastic Processes
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Author : Yuichiro Kakihara
language : en
Publisher: World Scientific
Release Date : 1997-02-27
Multidimensional Second Order Stochastic Processes written by Yuichiro Kakihara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-02-27 with Mathematics categories.
This book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or time series. 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 and also the stationary class. Emphasis is on the use of functional, 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. Readers may find that the covariance kernel analysis is emphasized and it reveals another aspect of stochastic processes. This book is intended not only for probabilists and statisticians, but also for communication engineers.
Stochastic Processes Harmonizable Theory
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Author : Malempati Madhusudana Rao
language : en
Publisher: World Scientific
Release Date : 2020-09-21
Stochastic Processes Harmonizable Theory written by Malempati Madhusudana Rao and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-21 with Mathematics categories.
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
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Author : Yuichiro Kakihara
language : en
Publisher: World Scientific
Release Date : 2021-07-29
Hilbert And Banach Space Valued Stochastic Processes written by Yuichiro Kakihara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-29 with Mathematics categories.
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
language : en
Publisher: World Scientific
Release Date : 2022-12-06
Harmonic Analysis On Hypergroups Approximation And Stochastic Sequences written by Rupert Lasser and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.
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.
Structural Aspects In The Theory Of Probability
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Author : Herbert Heyer
language : en
Publisher: World Scientific
Release Date : 2010
Structural Aspects In The Theory Of Probability written by Herbert Heyer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
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.
Using The Mathematics Literature
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Author : Kristine K. Fowler
language : en
Publisher: CRC Press
Release Date : 2004-05-25
Using The Mathematics Literature written by Kristine K. Fowler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05-25 with Language Arts & Disciplines categories.
This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.
Stochastic Processes And Functional Analysis
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Author : Alan C. Krinik
language : en
Publisher: CRC Press
Release Date : 2004-03-23
Stochastic Processes And Functional Analysis written by Alan C. Krinik and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-23 with Mathematics categories.
This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochas
A Step By Step Approach To Using Sas For Univariate Multivariate Statistics
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Author : Norm O'Rourke
language : en
Publisher: SAS Institute
Release Date : 2005
A Step By Step Approach To Using Sas For Univariate Multivariate Statistics written by Norm O'Rourke and has been published by SAS Institute this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
Providing practice data inspired by actual studies, this book explains how to choose the right statistic, understand the assumptions underlying the procedure, prepare an SAS program for an analysis, interpret the output, and summarize the analysis and results according to the format prescribed in the Publication Manual of the American Psychological Association.
Groundwater Contaminant Transport
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Author : F.B.J. Barends
language : en
Publisher: Routledge
Release Date : 2017-07-12
Groundwater Contaminant Transport written by F.B.J. Barends and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-12 with Technology & Engineering categories.
Impacts of developed tools of heterogenous characterization on the hydrodynamics of flow and the transport mechanisms are illustrated in this text through a series of extensive numerical simulations consisting of single and multiple-realizations (Monte Carlo method).
Markov Operators Positive Semigroups And Approximation Processes
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Author : Francesco Altomare
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2015-12-18
Markov Operators Positive Semigroups And Approximation Processes written by Francesco Altomare and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-18 with Mathematics categories.
This research monograph gives a detailed account of a theory which is mainly concerned with certain classes of degenerate differential operators, Markov semigroups and approximation processes. These mathematical objects are generated by arbitrary Markov operators acting on spaces of continuous functions defined on compact convex sets; the study of the interrelations between them constitutes one of the distinguishing features of the book. Among other things, this theory provides useful tools for studying large classes of initial-boundary value evolution problems, the main aim being to obtain a constructive approximation to the associated positive C0-semigroups by means of iterates of suitable positive approximating operators. As a consequence, a qualitative analysis of the solutions to the evolution problems can be efficiently developed. The book is mainly addressed to research mathematicians interested in modern approximation theory by positive linear operators and/or in the theory of positive C0-semigroups of operators and evolution equations. It could also serve as a textbook for a graduate level course.