Author: Willliam Feller
Publisher: John Wiley & Sons
ISBN: 9788126518067
Page: 700
View: 8592

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· The Exponential and the Uniform Densities· Special Densities. Randomization· Densities in Higher Dimensions. Normal Densities and Processes· Probability Measures and Spaces· Probability Distributions in Rr· A Survey of Some Important Distributions and Processes· Laws of Large Numbers. Applications in Analysis· The Basic Limit Theorems· Infinitely Divisible Distributions and Semi-Groups· Markov Processes and Semi-Groups· Renewal Theory· Random Walks in R1· Laplace Transforms. Tauberian Theorems. Resolvents· Applications of Laplace Transforms· Characteristic Functions· Expansions Related to the Central Limit Theorem,· Infinitely Divisible Distributions· Applications of Fourier Methods to Random Walks· Harmonic Analysis

A First Look at Rigorous Probability Theory

Author: Jeffrey Seth Rosenthal
Publisher: World Scientific
ISBN: 9812703705
Category: Mathematics
Page: 219
View: 9724

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Features an introduction to probability theory using measure theory. This work provides proofs of the essential introductory results and presents the measure theory and mathematical details in terms of intuitive probabilistic concepts, rather than as separate, imposing subjects.

Grundbegriffe der Wahrscheinlichkeitsrechnung

Author: A. Kolomogoroff
Publisher: Springer-Verlag
ISBN: 3642498884
Category: Mathematics
Page: 62
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

An Introduction to Bootstrap Methods with Applications to R

Author: Michael R. Chernick,Robert A. LaBudde
Publisher: John Wiley & Sons
ISBN: 1118625412
Category: Mathematics
Page: 240
View: 6904

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A comprehensive introduction to bootstrap methods in the Rprogramming environment Bootstrap methods provide a powerful approach to statisticaldata analysis, as they have more general applications than standardparametric methods. An Introduction to Bootstrap Methods withApplications to R explores the practicality of this approach andsuccessfully utilizes R to illustrate applications for thebootstrap and other resampling methods. This book provides a modernintroduction to bootstrap methods for readers who do not have anextensive background in advanced mathematics. Emphasis throughoutis on the use of bootstrap methods as an exploratory tool,including its value in variable selection and other modelingenvironments. The authors begin with a description of bootstrap methods andits relationship to other resampling methods, along with anoverview of the wide variety of applications of the approach.Subsequent chapters offer coverage of improved confidence setestimation, estimation of error rates in discriminant analysis, andapplications to a wide variety of hypothesis testing and estimationproblems, including pharmaceutical, genomics, and economics. Toinform readers on the limitations of the method, the book alsoexhibits counterexamples to the consistency of bootstrapmethods. An introduction to R programming provides the needed preparationto work with the numerous exercises and applications presentedthroughout the book. A related website houses the book's Rsubroutines, and an extensive listing of references providesresources for further study. Discussing the topic at a remarkably practical and accessiblelevel, An Introduction to Bootstrap Methods with Applications to Ris an excellent book for introductory courses on bootstrap andresampling methods at the upper-undergraduate and graduate levels.It also serves as an insightful reference for practitioners workingwith data in engineering, medicine, and the social sciences whowould like to acquire a basic understanding of bootstrapmethods.


Einführung in die Wahrscheinlichkeitstheorie und Statistik
Author: Hans-Otto Georgii
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110359707
Category: Mathematics
Page: 448
View: 1948

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Dieses Lehrbuch gibt eine Einführung in die "Mathematik des Zufalls", bestehend aus den beiden Teilbereichen Wahrscheinlichkeitstheorie und Statistik. Die stochastischen Konzepte, Modelle und Methoden werden durch typische Anwendungsbeispiele motiviert und anschließend systematisch entwickelt. Der dafür notwendige maßtheoretische Rahmen wird gleich zu Beginn auf elementarem Niveau bereitgestellt. Zahlreiche Übungsaufgaben, zum Teil mit Lösungsskizzen, illustrieren und ergänzen den Text. Zielgruppe sind Studierende der Mathematik ab dem dritten Semester, sowie Naturwissenschaftler und Informatiker mit Interesse an den mathematischen Grundlagen der Stochastik. Die 5. Auflage wurde nochmals bearbeitet und maßvoll ergänzt.

Option Pricing and Estimation of Financial Models with R

Author: Stefano M. Iacus
Publisher: John Wiley & Sons
ISBN: 9781119990208
Category: Business & Economics
Page: 472
View: 7101

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Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.

Statistical Methods in Radio Wave Propagation

Proceedings of a Symposium Held at the University of California, Los Angeles, June 18–20, 1958
Author: W. C. Hoffman
Publisher: Elsevier
ISBN: 1483154157
Category: Technology & Engineering
Page: 348
View: 4795

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Statistical Methods in Radio Wave Propagation contains the proceedings of a symposium held at the University of California, Los Angeles, on June 18-20, 1958. The papers explore the use of statistical techniques in the analysis and interpretation of data pertaining to the propagation of radio waves. The discussion is organized around three themes: statistical theory and methodology; radio propagation phenomena having a joint statistical and physical structure; and instrumentation. This book is comprised of 23 chapters and begins by summarizing the principal results of a series of statistical studies on the intensity distributions due to rapid fading. The reader is then introduced to some theoretical investigations on fading phenomena; radio-measurement of ionospheric drift as a problem in parameter estimation; the propagation of random radiation in free space; and the statistics of working spells and periods of breakdown for a number of radio links in series. The remaining chapters deal with airborne measurements of tropospheric index of refraction fluctuations; the distribution of the fade lengths of a randomly fading radio signal; diversity statistics in scatter propagation; and extrapolation of spatial correlation functions. The final chapter describes a rapid statistical data processing system for radio propagation research. This monograph will be a useful resource for both radio scientists and statisticians.

Fundamentals of Queueing Theory

Author: Donald Gross,John F. Shortle,James M. Thompson,Carl M. Harris
Publisher: John Wiley & Sons
ISBN: 1118211642
Category: Mathematics
Page: 528
View: 9141

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Praise for the Third Edition "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented." —IIE Transactions on Operations Engineering Thoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research. This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include: Retrial queues Approximations for queueing networks Numerical inversion of transforms Determining the appropriate number of servers to balance quality and cost of service Each chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site. With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

A Graduate Course in Probability

Author: Howard G. Tucker
Publisher: Academic Press
ISBN: 1483220508
Category: Mathematics
Page: 288
View: 8457

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Probability and Mathematical Statistics: A Series of Monographs and Textbooks: A Graduate Course in Probability presents some of the basic theorems of analytic probability theory in a cohesive manner. This book discusses the probability spaces and distributions, stochastic independence, basic limiting operations, and strong limit theorems for independent random variables. The central limit theorem, conditional expectation and martingale theory, and Brownian motion are also elaborated. The prerequisite for this text is knowledge of real analysis or measure theory, particularly the Lebesgue dominated convergence theorem, Fubini's theorem, Radon-Nikodym theorem, Egorov's theorem, monotone convergence theorem, and theorem on unique extension of a sigma-finite measure from an algebra to the sigma-algebra generated by it. This publication is suitable for a one-year graduate course in probability given in a mathematics program and preferably for students in their second year of graduate work.

Probability and Measure

Author: Patrick Billingsley
Publisher: John Wiley & Sons
ISBN: 1118341910
Category: Mathematics
Page: 656
View: 7884

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Praise for the Third Edition "It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (, January 2006) A complete and comprehensive classic in probability and measure theory Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years. Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this Anniversary Edition builds on its strong foundation of measure theory and probability with Billingsley's unique writing style. In recognition of 35 years of publication, impacting tens of thousands of readers, this Anniversary Edition has been completely redesigned in a new, open and user-friendly way in order to appeal to university-level students. This book adds a new foreward by Steve Lally of the Statistics Department at The University of Chicago in order to underscore the many years of successful publication and world-wide popularity and emphasize the educational value of this book. The Anniversary Edition contains features including: An improved treatment of Brownian motion Replacement of queuing theory with ergodic theory Theory and applications used to illustrate real-life situations Over 300 problems with corresponding, intensive notes and solutions Updated bibliography An extensive supplement of additional notes on the problems and chapter commentaries Patrick Billingsley was a first-class, world-renowned authority in probability and measure theory at a leading U.S. institution of higher education. He continued to be an influential probability theorist until his unfortunate death in 2011. Billingsley earned his Bachelor's Degree in Engineering from the U.S. Naval Academy where he served as an officer. he went on to receive his Master's Degree and doctorate in Mathematics from Princeton University.Among his many professional awards was the Mathematical Association of America's Lester R. Ford Award for mathematical exposition. His achievements through his long and esteemed career have solidified Patrick Billingsley's place as a leading authority in the field and been a large reason for his books being regarded as classics. This Anniversary Edition of Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability. Like the previous editions, this Anniversary Edition is a key resource for students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.

Integration and Probability

Author: Paul Malliavin
Publisher: Springer Science & Business Media
ISBN: 1461242029
Category: Mathematics
Page: 326
View: 4433

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An introduction to analysis with the right mix of abstract theories and concrete problems. Starting with general measure theory, the book goes on to treat Borel and Radon measures and introduces the reader to Fourier analysis in Euclidean spaces with a treatment of Sobolev spaces, distributions, and the corresponding Fourier analysis. It continues with a Hilbertian treatment of the basic laws of probability including Doob's martingale convergence theorem and finishes with Malliavin's "stochastic calculus of variations" developed in the context of Gaussian measure spaces. This invaluable contribution gives a taste of the fact that analysis is not a collection of independent theories, but can be treated as a whole.

An Introduction to Measure-Theoretic Probability

Author: George G. Roussas
Publisher: Academic Press
ISBN: 0128002905
Category: Mathematics
Page: 426
View: 4114

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An Introduction to Measure-Theoretic Probability, Second Edition, employs a classical approach to teaching the basics of measure theoretic probability. This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics, probability and other related areas should be equipped with. This edition requires no prior knowledge of measure theory, covers all its topics in great detail, and includes one chapter on the basics of ergodic theory and one chapter on two cases of statistical estimation. Topics range from the basic properties of a measure to modes of convergence of a sequence of random variables and their relationships; the integral of a random variable and its basic properties; standard convergence theorems; standard moment and probability inequalities; the Hahn-Jordan Decomposition Theorem; the Lebesgue Decomposition T; conditional expectation and conditional probability; theory of characteristic functions; sequences of independent random variables; and ergodic theory. There is a considerable bend toward the way probability is actually used in statistical research, finance, and other academic and nonacademic applied pursuits. Extensive exercises and practical examples are included, and all proofs are presented in full detail. Complete and detailed solutions to all exercises are available to the instructors on the book companion site. This text will be a valuable resource for graduate students primarily in statistics, mathematics, electrical and computer engineering or other information sciences, as well as for those in mathematical economics/finance in the departments of economics. Provides in a concise, yet detailed way, the bulk of probabilistic tools essential to a student working toward an advanced degree in statistics, probability, and other related fields Includes extensive exercises and practical examples to make complex ideas of advanced probability accessible to graduate students in statistics, probability, and related fields All proofs presented in full detail and complete and detailed solutions to all exercises are available to the instructors on book companion site Considerable bend toward the way probability is used in statistics in non-mathematical settings in academic, research and corporate/finance pursuits.

Advanced Linear Algebra

Author: Steven Roman
Publisher: Springer Science & Business Media
ISBN: 0387728317
Category: Mathematics
Page: 525
View: 9975

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This graduate level textbook covers an especially broad range of topics. The book first offers a careful discussion of the basics of linear algebra. It then proceeds to a discussion of modules, emphasizing a comparison with vector spaces, and presents a thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory, culminating in the finite dimensional spectral theorem for normal operators. The new edition has been revised and contains a chapter on the QR decomposition, singular values and pseudoinverses, and a chapter on convexity, separation and positive solutions to linear systems.

An Introduction to Probability Theory and Its Applications

Author: William Feller
Publisher: John Wiley & Sons
Category: Mathematics
Page: 704
View: 9616

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The exponential and the uniform densities; Special densities. Randomization; Densities in higher dimensions. Normal densities and processes; Probability measures and spaces; Probability distributions in Rr; A survey of some important distributions and processes; Laws of large numbers. Aplications in analysis; The basic limit theorems; Infinitely divisible distributions and semi-groups; Markov processes and semi-groups; Renewal theory; Random walks in R1; Laplace transforms. Tauberian theorems. Resolvents; Aplications of Laplace transforms; Characteristic functions; Expansions related to the central limit theorem; Infinitely divisible distributions; Applications of Fourier methods to ramdom walks; harmonic analysis; Answers to problems.

An Introduction to Operators on the Hardy-Hilbert Space

Author: Ruben A. Martinez-Avendano,Peter Rosenthal
Publisher: Springer Science & Business Media
ISBN: 0387485783
Category: Mathematics
Page: 220
View: 9437

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This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.

Fundamentals of Applied Probability and Random Processes

Author: Oliver Ibe
Publisher: Elsevier
ISBN: 0080492703
Category: Mathematics
Page: 456
View: 4809

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This book is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study. * Good and solid introduction to probability theory and stochastic processes * Logically organized; writing is presented in a clear manner * Choice of topics is comprehensive within the area of probability * Ample homework problems are organized into chapter sections

Additive Number Theory: Inverse Problems and the Geometry of Sumsets

Author: Melvyn B. Nathanson
Publisher: Springer Science & Business Media
ISBN: 9780387946559
Category: Mathematics
Page: 296
View: 7420

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Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer H -> 2, and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. By contrast, in an inverse problem, one starts with a sumset hA, and attempts to describe the structure of the underlying set A. In recent years there has been ramrkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plünnecke, Vosper, and others. This volume includes their results, and culminates with an elegant proof by Ruzsa of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression.

Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

Author: Kai L. Chung
Publisher: Springer-Verlag
ISBN: 3642670334
Category: Mathematics
Page: 346
View: 7790

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Aus den Besprechungen: "Unter den zahlreichen Einführungen in die Wahrscheinlichkeitsrechnung bildet dieses Buch eine erfreuliche Ausnahme. Der Stil einer lebendigen Vorlesung ist über Niederschrift und Übersetzung hinweg erhalten geblieben. In jedes Kapitel wird sehr anschaulich eingeführt. Sinn und Nützlichkeit der mathematischen Formulierungen werden den Lesern nahegebracht. Die wichtigsten Zusammenhänge sind als mathematische Sätze klar formuliert." #FREQUENZ#1