The Borel Cantelli Lemma

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The Borel-Cantelli Lemma

Tapas Kumar Chandra
The Borel Cantelli Lemma Book PDF

Author : Tapas Kumar Chandra
Publisher : Springer Science & Business Media
Page : 114 pages
File Size : 54,8 Mb
Release : 2012-07-04
Category : Mathematics
ISBN : 9788132206774

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The Borel-Cantelli Lemma by Tapas Kumar Chandra Pdf

This monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it embodies the classical versions of these lemma, together with the well known as well as the most recent extensions of them due to Barndorff-Nielsen, Balakrishnan and Stepanov, Erdos and Renyi, Kochen and Stone, Petrov and the present author. The versions of the second Borel-Cantelli Lemma for pair wise negative quadrant dependent sequences, weakly *-mixing sequences, mixing sequences (due to Renyi) and for many other dependent sequences are all included. The special feature of the book is a detailed discussion of a strengthened form of the second Borel-Cantelli Lemma and the conditional form of the Borel-Cantelli Lemmas due to Levy, Chen and Serfling. All these results are well illustrated by means of many interesting examples. All the proofs are rigorous, complete and lucid. An extensive list of research papers, some of which are forthcoming, is provided. The book can be used for a self study and as an invaluable research reference on the present topic.

Probability

Rick Durrett
Probability Book PDF

Author : Rick Durrett
Publisher : Cambridge University Press
Page : 128 pages
File Size : 50,9 Mb
Release : 2010-08-30
Category : Mathematics
ISBN : 9781139491136

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Probability by Rick Durrett Pdf

This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Probability Space

Nancy Kress
Probability Space Book PDF

Author : Nancy Kress
Publisher : Tor Books
Page : 368 pages
File Size : 48,8 Mb
Release : 2004-01-05
Category : Fiction
ISBN : 9781466825253

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Probability Space by Nancy Kress Pdf

Nancy Kress cemented her reputation in SF with the publication of her multiple-award–winning novella, "Beggars in Spain," which became the basis for her extremely successful Beggars Trilogy (comprising Beggars in Spain, Beggars and Choosers, and Beggars Ride). And now she brings us Probability Space, the conclusion of the trilogy that began with Probability Moon and then Probability Sun, which is centered on the same world as Kress's Nebula Award-winning novelette, "Flowers of Aulit Prison." The Probability Trilogy has already been widely recognized as the next great work by this important SF writer. In Probability Space, humanity's war with the alien Fallers continues, and it is a war we are losing. Our implacable foes ignore all attempts at communication, and they take no prisoners. Our only hope lies with an unlikely coalition: Major Lyle Kaufman, retired warrior; Marbet Grant, the Sensitive who's involved with Kaufman; Amanda, a very confused fourteen-year-old girl; and Magdalena, one of the biggest power brokers in all of human space. As the action moves from Earth to Mars to the farthest reaches of known space, with civil unrest back home and alien war in deep space, four humans--armed with little more than an unproven theory--try to enter the Fallers' home star system. It's a desperate gamble, and the fate of the entire universe may hang in the balance. At the Publisher's request, this title is being sold without Digital Rights Management Software (DRM) applied.

An Introduction to Measure Theory

Terence Tao
An Introduction to Measure Theory Book PDF

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 206 pages
File Size : 41,5 Mb
Release : 2021-09-03
Category : Education
ISBN : 9781470466404

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An Introduction to Measure Theory by Terence Tao Pdf

This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Real Analysis (Classic Version)

Halsey Royden,Patrick Fitzpatrick
Real Analysis Classic Version Book PDF

Author : Halsey Royden,Patrick Fitzpatrick
Publisher : Pearson Modern Classics for Advanced Mathematics Series
Page : 0 pages
File Size : 42,7 Mb
Release : 2017-02-13
Category : Functional analysis
ISBN : 0134689496

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Real Analysis (Classic Version) by Halsey Royden,Patrick Fitzpatrick Pdf

This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.

Probability: A Graduate Course

Allan Gut
Probability A Graduate Course Book PDF

Author : Allan Gut
Publisher : Springer Science & Business Media
Page : 617 pages
File Size : 51,8 Mb
Release : 2006-03-16
Category : Mathematics
ISBN : 9780387273327

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Probability: A Graduate Course by Allan Gut Pdf

This textbook on the theory of probability starts from the premise that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by explanations of the three main subjects in probability: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales.

High-Dimensional Probability

Roman Vershynin
High Dimensional Probability Book PDF

Author : Roman Vershynin
Publisher : Cambridge University Press
Page : 299 pages
File Size : 53,6 Mb
Release : 2018-09-27
Category : Business & Economics
ISBN : 9781108415194

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High-Dimensional Probability by Roman Vershynin Pdf

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.

Probability and Measure

Patrick Billingsley
Probability and Measure Book PDF

Author : Patrick Billingsley
Publisher : John Wiley & Sons
Page : 612 pages
File Size : 42,5 Mb
Release : 2017
Category : Electronic
ISBN : 8126517719

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Probability and Measure by Patrick Billingsley Pdf

Now in its new third edition, Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Retaining the unique approach of the previous editions, this text interweaves material on probability and measure, so that probability problems generate an interest in measure theory and measure theory is then developed and applied to probability. Probability and Measure provides thorough coverage of probability, measure, integration, random variables and expected values, convergence of distributions, derivatives and conditional probability, and stochastic processes. The Third Edition features an improved treatment of Brownian motion and the replacement of queuing theory with ergodic theory.· Probability· Measure· Integration· Random Variables and Expected Values· Convergence of Distributions· Derivatives and Conditional Probability· Stochastic Processes

A Course in Large Sample Theory

Thomas S. Ferguson
A Course in Large Sample Theory Book PDF

Author : Thomas S. Ferguson
Publisher : Routledge
Page : 140 pages
File Size : 50,7 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9781351470056

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A Course in Large Sample Theory by Thomas S. Ferguson Pdf

A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.

Brownian Motion

Peter Mörters,Yuval Peres
Brownian Motion Book PDF

Author : Peter Mörters,Yuval Peres
Publisher : Cambridge University Press
Page : 128 pages
File Size : 48,7 Mb
Release : 2010-03-25
Category : Mathematics
ISBN : 9781139486576

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Brownian Motion by Peter Mörters,Yuval Peres Pdf

This eagerly awaited textbook covers everything the graduate student in probability wants to know about Brownian motion, as well as the latest research in the area. Starting with the construction of Brownian motion, the book then proceeds to sample path properties like continuity and nowhere differentiability. Notions of fractal dimension are introduced early and are used throughout the book to describe fine properties of Brownian paths. The relation of Brownian motion and random walk is explored from several viewpoints, including a development of the theory of Brownian local times from random walk embeddings. Stochastic integration is introduced as a tool and an accessible treatment of the potential theory of Brownian motion clears the path for an extensive treatment of intersections of Brownian paths. An investigation of exceptional points on the Brownian path and an appendix on SLE processes, by Oded Schramm and Wendelin Werner, lead directly to recent research themes.

MEASURE THEORY AND PROBABILITY

A. K. BASU
MEASURE THEORY AND PROBABILITY Book PDF

Author : A. K. BASU
Publisher : PHI Learning Pvt. Ltd.
Page : 233 pages
File Size : 40,7 Mb
Release : 2012-04-21
Category : Mathematics
ISBN : 9788120343856

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MEASURE THEORY AND PROBABILITY by A. K. BASU Pdf

This compact and well-received book, now in its second edition, is a skilful combination of measure theory and probability. For, in contrast to many books where probability theory is usually developed after a thorough exposure to the theory and techniques of measure and integration, this text develops the Lebesgue theory of measure and integration, using probability theory as the motivating force. What distinguishes the text is the illustration of all theorems by examples and applications. A section on Stieltjes integration assists the student in understanding the later text better. For easy understanding and presentation, this edition has split some long chapters into smaller ones. For example, old Chapter 3 has been split into Chapters 3 and 9, and old Chapter 11 has been split into Chapters 11, 12 and 13. The book is intended for the first-year postgraduate students for their courses in Statistics and Mathematics (pure and applied), computer science, and electrical and industrial engineering. KEY FEATURES : Measure theory and probability are well integrated. Exercises are given at the end of each chapter, with solutions provided separately. A section is devoted to large sample theory of statistics, and another to large deviation theory (in the Appendix).

The Doctrine of Chances

Stewart N. Ethier
The Doctrine of Chances Book PDF

Author : Stewart N. Ethier
Publisher : Springer Science & Business Media
Page : 822 pages
File Size : 46,5 Mb
Release : 2010-05-19
Category : Mathematics
ISBN : 9783540787839

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The Doctrine of Chances by Stewart N. Ethier Pdf

Three centuries ago Montmort and De Moivre published two books on probability theory emphasizing its most important application at that time, games of chance. This book, on the probabilistic aspects of gambling, is a modern version of those classics.

Probability

Davar Khoshnevisan
Probability Book PDF

Author : Davar Khoshnevisan
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 45,7 Mb
Release : 2007
Category : Probabilities
ISBN : 9780821842157

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Probability by Davar Khoshnevisan Pdf

This is a textbook for a one-semester graduate course in measure-theoretic probability theory, but with ample material to cover an ordinary year-long course at a more leisurely pace. Khoshnevisan's approach is to develop the ideas that are absolutely central to modern probability theory, and to showcase them by presenting their various applications. As a result, a few of the familiar topics are replaced by interesting non-standard ones. The topics range from undergraduate probability and classical limit theorems to Brownian motion and elements of stochastic calculus. Throughout, the reader will find many exciting applications of probability theory and probabilistic reasoning. There are numerous exercises, ranging from the routine to the very difficult. Each chapter concludes with historical notes.

Real Analysis with Economic Applications

Efe A. Ok
Real Analysis with Economic Applications Book PDF

Author : Efe A. Ok
Publisher : Princeton University Press
Page : 832 pages
File Size : 48,5 Mb
Release : 2011-09-05
Category : Business & Economics
ISBN : 9781400840892

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Real Analysis with Economic Applications by Efe A. Ok Pdf

There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.

Continued Fractions

A. M. Rockett,Peter Szsz
Continued Fractions Book PDF

Author : A. M. Rockett,Peter Szsz
Publisher : World Scientific
Page : 202 pages
File Size : 42,5 Mb
Release : 1992-08-01
Category : Mathematics
ISBN : 9810210523

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Continued Fractions by A. M. Rockett,Peter Szsz Pdf

This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.