Menu Close

Strong Limit Theorems

These are the books for those you who looking for to read the Strong Limit Theorems, try to read or download Pdf/ePub books and some of authors may have disable the live reading. Check the book if it available for your country and user who already subscribe will have full access all free books from the library source.

Strong Limit Theorems

Strong Limit Theorems [Pdf/ePub] eBook

Strong Limit Theorems by Lin Zhengyan,Lu Zhuarong Book Summary:

This volume presents an up-to-date review of the most significant developments in strong Approximation and strong convergence in probability theory. The book consists of three chapters. The first deals with Wiener and Gaussian processes. Chapter 2 is devoted to the increments of partial sums of independent random variables. Chapter 3 concentrates on the strong laws of processes generated by infinite-dimensional Ornstein-Uhlenbeck processes. For researchers whose work involves probability theory and statistics.

Strong Limit Theorems in Noncommutative L2-Spaces

Strong Limit Theorems [Pdf/ePub] eBook

Strong Limit Theorems in Noncommutative L2-Spaces by Ryszard Jajte Book Summary:

The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.

Limit Theorems for Multi-Indexed Sums of Random Variables

Strong Limit Theorems [Pdf/ePub] eBook

Limit Theorems for Multi-Indexed Sums of Random Variables by Oleg Klesov Book Summary:

Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in the classical setting, as well as some new approaches that are simpler than those already established in the literature. In particular, new proofs of the strong law of large numbers and the Hajek-Renyi inequality are detailed. Applications of the described theory include Gibbs fields, spin glasses, polymer models, image analysis and random shapes. Limit theorems form the backbone of probability theory and statistical theory alike. The theory of multiple sums of random variables is a direct generalization of the classical study of limit theorems, whose importance and wide application in science is unquestionable. However, to date, the subject of multiple sums has only been treated in journals. The results described in this book will be of interest to advanced undergraduates, graduate students and researchers who work on limit theorems in probability theory, the statistical analysis of random fields, as well as in the field of random sets or stochastic geometry. The central topic is also important for statistical theory, developing statistical inferences for random fields, and also has applications to the sciences, including physics and chemistry.

Advanced Technology in Teaching - Proceedings of the 2009 3rd International Conference on Teaching and Computational Science (WTCS 2009)

Strong Limit Theorems [Pdf/ePub] eBook

Advanced Technology in Teaching - Proceedings of the 2009 3rd International Conference on Teaching and Computational Science (WTCS 2009) by Yanwen Wu Book Summary:

The volume includes a set of selected papers extended and revised from the International Conference on Teaching and Computational Science (WTCS 2009) held on December 19- 20, 2009, Shenzhen, China. WTCS 2009 best papers Volume 1 is to provide a forum for researchers, educators, engineers, and government officials involved in the general areas of Intelligent Ubiquitous Computing and Education to disseminate their latest research results and exchange views on the future research directions of these fields. 128 high-quality papers are included in the volume. Each paper has been peer-reviewed by at least 2 program committee members and selected by the volume editor Prof.Wu. On behalf of the WTCS 2009, we would like to express our sincere appreciation to all of authors and referees for their efforts reviewing the papers. Hoping you can find lots of profound research ideas and results on the related fields of Intelligent Ubiquitous Computing and Education.

Probability in Banach Spaces

Strong Limit Theorems [Pdf/ePub] eBook

Probability in Banach Spaces by Michel Ledoux,Michel Talagrand Book Summary:

Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed.

Probability Theory and Mathematical Statistics

Strong Limit Theorems [Pdf/ePub] eBook

Probability Theory and Mathematical Statistics by Bronius Grigelionis Book Summary:

This Proceedings volume contains a selection of invited and other papers by international scientists which were presented at the VIth International Vilnius Conference on Probability Theory and Mathematical Statistics, held in Vilnius, Lithuania, 28 June--3 July, 1993. The main topics of the conference were: limit theorems, stochastic analysis and stochastic physics, quantum probability theory, statistics, change detection in random processes, and probabilistic number theory.

A Graduate Course in Probability

Strong Limit Theorems [Pdf/ePub] eBook

A Graduate Course in Probability by Howard G. Tucker Book Summary:

"Suitable for a graduate course in analytic probability, this text requires only a limited background in real analysis. Topics include probability spaces and distributions, stochastic independence, basic limiting options, strong limit theorems for independent random variables, central limit theorem, conditional expectation and Martingale theory, and an introduction to stochastic processes"--

Classical Summation in Commutative and Noncommutative Lp-Spaces

Strong Limit Theorems [Pdf/ePub] eBook

Classical Summation in Commutative and Noncommutative Lp-Spaces by Andreas Defant Book Summary:

The aim of this research is to develop a systematic scheme that makes it possible to transform important parts of the by now classical theory of summation of general orthonormal series into a similar theory for series in noncommutative $L_p$-spaces constructed over a noncommutative measure space (a von Neumann algebra of operators acting on a Hilbert space together with a faithful normal state on this algebra).

Probability Theory

Strong Limit Theorems [Pdf/ePub] eBook

Probability Theory by Vincent F. Hendricks,Stig Andur Pedersen,Klaus Frovin Jørgensen Book Summary:

A collection of papers presented at the conference on Probability Theory - Philosophy, Recent History and Relations to Science, University of Roskilde, Denmark, September 16-18, 1998. Since the measure theoretical definition of probability was proposed by Kolmogorov, probability theory has developed into a mature mathematical theory. It is today a fruitful field of mathematics that has important applications in philosophy, science, engineering, and many other areas. The measure theoretical definition of probability and its axioms, however, are not without their problems; some of them even puzzled Kolmogorov. This book sheds light on some recent discussions of the problems in probability theory and their history, analysing their philosophical and mathematical significance, and the role pf mathematical probability theory in other sciences.

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables

Strong Limit Theorems [Pdf/ePub] eBook

Asymptotic Behaviour of Linearly Transformed Sums of Random Variables by V.V. Buldygin,Serguei Solntsev Book Summary:

Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently.

Proceedings of the Bakuriani Colloquium in Honour of Yu. V. Prohorov

Strong Limit Theorems [Pdf/ePub] eBook

Proceedings of the Bakuriani Colloquium in Honour of Yu. V. Prohorov by Vâčeslav Viktorovič Sazonov,T. L. Shervashidze Book Summary:

Download or read Proceedings of the Bakuriani Colloquium in Honour of Yu. V. Prohorov book by clicking button below to visit the book download website. There are multiple format available for you to choose (Pdf, ePub, Doc).

Fundamentals of Hyperbolic Manifolds

Strong Limit Theorems [Pdf/ePub] eBook

Fundamentals of Hyperbolic Manifolds by R. D. Canary,A. Marden,D. B. A. Epstein Book Summary:

Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

The Concentration of Measure Phenomenon

Strong Limit Theorems [Pdf/ePub] eBook

The Concentration of Measure Phenomenon by Michel Ledoux Book Summary:

It was undoubtedly a necessary task to collect all the results on the concentration of measure during the past years in a monograph. The author did this very successfully and the book is an important contribution to the topic. It will surely influence further research in this area considerably. The book is very well written, and it was a great pleasure for the reviewer to read it. --Mathematical Reviews The observation of the concentration of measure phenomenon is inspired by isoperimetric inequalities. A familiar example is the way the uniform measure on the standard sphere $S^n$ becomes concentrated around the equator as the dimension gets large. This property may be interpreted in terms of functions on the sphere with small oscillations, an idea going back to Levy. The phenomenon also occurs in probability, as a version of the law of large numbers, due to Emile Borel. This book offers the basic techniques and examples of the concentration of measure phenomenon. The concentration of measure phenomenon was put forward in the early seventies by V. Milman in the asymptotic geometry of Banach spaces. It is of powerful interest in applications in various areas, such as geometry, functional analysis and infinite-dimensional integration, discrete mathematics and complexity theory, and probability theory. Particular emphasis is on geometric, functional, and probabilistic tools to reach and describe measure concentration in a number of settings. The book presents concentration functions and inequalities, isoperimetric and functional examples, spectrum and topological applications, product measures, entropic and transportation methods, as well as aspects of M. Talagrand's deep investigation of concentration in product spaces and its application in discrete mathematics and probability theory, supremum of Gaussian and empirical processes, spin glass, random matrices, etc. Prerequisites are a basic background in measure theory, functional analysis, and probability theory.

Fractional Fields and Applications

Strong Limit Theorems [Pdf/ePub] eBook

Fractional Fields and Applications by Serge Cohen,Jacques Istas Book Summary:

This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields. The Lévy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'être of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.

Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables

Strong Limit Theorems [Pdf/ePub] eBook

Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables by Shoumei Li,Y. Ogura,V. Kreinovich,Vladik Kreinovich Book Summary:

This book presents a clear, systematic treatment of convergence theorems of set-valued random variables (random sets) and fuzzy set-valued random variables (random fuzzy sets). Topics such as strong laws of large numbers and central limit theorems, including new results in connection with the theory of empirical processes are covered. The author's own recent developments on martingale convergence theorems and their applications to data processing are also included. The mathematical foundations along with a clear explanation such as Hölmander's embedding theorem, notions of various convergence of sets and fuzzy sets, Aumann integrals, conditional expectations, selection theorems, measurability and integrability arguments for both set-valued and fuzzy set-valued random variables and newly obtained optimizations techniques based on invariant properties are also given.

Selected Works of Murray Rosenblatt

Strong Limit Theorems [Pdf/ePub] eBook

Selected Works of Murray Rosenblatt by Richard A. Davis,Keh-Shin Lii,Dimitris N. Politis Book Summary:

During the second half of the 20th century, Murray Rosenblatt was one of the most celebrated and leading figures in probability and statistics. Among his many contributions, Rosenblatt conducted seminal work on density estimation, central limit theorems under strong mixing conditions, spectral domain methodology, long memory processes and Markov processes. He has published over 130 papers and 5 books, many as relevant today as when they first appeared decades ago. Murray Rosenblatt was one of the founding members of the Department of Mathematics at the University of California at San Diego (UCSD) and served as advisor to over twenty PhD students. He maintains a close association with UCSD in his role as Professor Emeritus. This volume is a celebration of Murray Rosenblatt's stellar research career that spans over six decades, and includes some of his most interesting and influential papers. Several leading experts provide commentary and reflections on various directions of Murray's research portfolio.

Associated Sequences, Demimartingales and Nonparametric Inference

Strong Limit Theorems [Pdf/ePub] eBook

Associated Sequences, Demimartingales and Nonparametric Inference by B.L.S. Prakasa Rao Book Summary:

This book gives a comprehensive review of results for associated sequences and demimartingales developed so far, with special emphasis on demimartingales and related processes. Probabilistic properties of associated sequences, demimartingales and related processes are discussed in the first six chapters. Applications of some of these results to some problems in nonparametric statistical inference for such processes are investigated in the last three chapters.

Time Series, Fuzzy Analysis and Miscellaneous Topics

Strong Limit Theorems [Pdf/ePub] eBook

Time Series, Fuzzy Analysis and Miscellaneous Topics by Madan Lal Puri Book Summary:

Professor Puri is one of the most versatile and prolific researchers in the world in mathematical statistics. His research areas include nonparametric statistics, order statistics, limit theory under mixing, time series, splines, tests of normality, generalized inverses of matrices and related topics, stochastic processes, statistics of directional data, random sets, and fuzzy sets and fuzzy measures. His fundamental contributions in developing new rank-based methods and precise evaluation of the standard procedures, asymptotic expansions of distributions of rank statistics, as well as large deviation results concerning them, span such areas as analysis of variance, analysis of covariance, multivariate analysis, and time series, to mention a few. His in-depth analysis has resulted in pioneering research contributions to prominent journals that have substantial impact on current research.This book together with the other two volumes (Volume 1: Nonparametric Methods in Statistics and Related Topics; Volume 2: Probability Theory and Extreme Value Theory), are a concerted effort to make his research works easily available to the research community. The sheer volume of the research output by him and his collaborators, coupled with the broad spectrum of the subject matters investigated, and the great number of outlets where the papers were published, attach special significance in making these works easily accessible.The papers selected for inclusion in this work have been classified into three volumes each consisting of several parts. All three volumes carry a final part consisting of the contents of the other two, as well as the complete list of Professor Puri's publications.